Append content without editing the whole page source. Let’s assume OA, OB and OC are three vectors as illustrated in the figure 1. {\displaystyle \left\|\mathbf {a} \right\|= {\sqrt {a_ {1}^ {2}+a_ {2}^ {2}+a_ {3}^ {2}}}} which is a consequence of the Pythagorean theorem since the basis vectors e1, e2, e3 are orthogonal unit vectors. Okay, then we need to compute the design off the angle that these two vectors forms. It corresponds to the L2-norm of the difference between the two vectors. $\vec {u} = (2, 3, 4, 2)$. Determine the Euclidean distance between $\vec{u} = (2, 3, 4, 2)$ and $\vec{v} = (1, -2, 1, 3)$. This victory. Recall that the squared Euclidean distance between any two vectors a and b is simply the sum of the square component-wise differences. View wiki source for this page without editing. View/set parent page (used for creating breadcrumbs and structured layout). The associated norm is called the Euclidean norm. The Euclidean distance between two vectors, A and B, is calculated as: Euclidean distance = √ Σ(A i-B i) 2. The distance between two vectors v and w is the length of the difference vector v - w. There are many different distance functions that you will encounter in the world. , x d ] and [ y 1 , y 2 , . So the norm of the vector to three minus one is just the square root off. We can then use this function to find the Euclidean distance between any two vectors: #define two vectors a <- c(2, 6, 7, 7, 5, 13, 14, 17, 11, 8) b <- c(3, 5, 5, 3, 7, 12, 13, 19, 22, 7) #calculate Euclidean distance between vectors euclidean(a, b) [1] 12.40967 The Euclidean distance between the two vectors turns out to be 12.40967. It is the most obvious way of representing distance between two points. If you want to discuss contents of this page - this is the easiest way to do it. The answers/resolutions are collected from stackoverflow, are licensed under Creative Commons Attribution-ShareAlike license. Basic Examples (2) Euclidean distance between two vectors: Euclidean distance between numeric vectors: scipy.spatial.distance.euclidean¶ scipy.spatial.distance.euclidean(u, v) [source] ¶ Computes the Euclidean distance between two 1-D arrays. The result is a positive distance value. A generalized term for the Euclidean norm is the L2 norm or L2 distance. Euclidean distance. $\endgroup$ – whuber ♦ Oct 2 '13 at 15:23 Each set of vectors is given as the columns of a matrix. This process is used to normalize the featuresÂ  Now I would like to compute the euclidean distance between x and y. I think the integer element is a problem because all other elements can get very close but the integer element has always spacings of ones. The euclidean distance matrix is matrix the contains the euclidean distance between each point across both matrices. This system utilizes Locality sensitive hashing (LSH) [50] for efficient visual feature matching. $d(\vec{u}, \vec{v}) = \| \vec{u} - \vec{v} \| = \sqrt{(u_1 - v_1)^2 + (u_2 - v_2)^2 ... (u_n - v_n)^2}$, $d(\vec{u}, \vec{v}) = d(\vec{v}, \vec{u})$, $d(\vec{u}, \vec{v}) = || \vec{u} - \vec{v} || = \sqrt{(u_1 - v_1)^2 + (u_2 - v_2)^2 ... (u_n - v_n)^2}$, $d(\vec{v}, \vec{u}) = || \vec{v} - \vec{u} || = \sqrt{(v_1 - u_1)^2 + (v_2 - u_2)^2 ... (v_n - u_n)^2}$, $(u_i - v_i)^2 = u_i^2 - 2u_iv_i + v_i^2 = v_i^2 - 2u_iv_i + 2u_i^2 = (v_i - u_i)^2$, $\vec{u}, \vec{v}, \vec{w} \in \mathbb{R}^n$, $d(\vec{u}, \vec{v}) \leq d(\vec{u}, \vec{w}) + d(\vec{w}, \vec{v})$, Creative Commons Attribution-ShareAlike 3.0 License. Euclidean distance Copyright ©document.write(new Date().getFullYear()); All Rights Reserved, How to make a search form with multiple search options in PHP, Google Drive API list files in folder v3 python, React component control another component, How to retrieve data from many-to-many relationship in hibernate, How to make Android app fit all screen sizes. , y d ] is radicaltp radicalvertex radicalvertex radicalbt d summationdisplay i =1 ( x i − y i ) 2 Here, each x i and y i is a random variable chosen uniformly in the range 0 to 1. Euclidean distance between two vectors, or between column vectors of two matrices. their Understand normalized squared euclidean distance?, Try to use z-score normalization on each set (subtract the mean and divide by standard deviation. Change the name (also URL address, possibly the category) of the page. Let’s discuss a few ways to find Euclidean distance by NumPy library. Directly comparing the Euclidean distance between two visual feature vectors in the high dimension feature space is not scalable. Euclidean distance, Euclidean distances, which coincide with our most basic physical idea of squared distance between two vectors x = [ x1 x2 ] and y = [ y1 y2 ] is the sum ofÂ  The Euclidean distance function measures the âas-the-crow-fliesâ distance. pdist2 is an alias for distmat, while pdist(X) is … It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance. The shortest path distance is a straight line. The points A, B and C form an equilateral triangle. The standardized Euclidean distance between two n-vectors u and v is $\sqrt{\sum {(u_i-v_i)^2 / V[x_i]}}.$ V is the variance vector; V[i] is the variance computed over all the i’th components of the points. These names come from the ancient Greek mathematicians Euclid and Pythagoras, although Euclid did not represent distances as numbers, and the connection from the Pythagorean theorem to distance calculation wa The following formula is used to calculate the euclidean distance between points. Euclidean metric is the “ordinary” straight-line distance between two points. So this is the distance between these two vectors. Ask Question Asked 1 year, 1 month ago. The corresponding loss function is the squared error loss (SEL), and places progressively greater weight on larger errors. I have the two image values G= [1x72] and G1 = [1x72]. I've been reading that the Euclidean distance between two points, and the dot product of theÂ  Dot Product, Lengths, and Distances of Complex Vectors For this problem, use the complex vectors. Click here to edit contents of this page. By using this metric, you can get a sense of how similar two documents or words are. and. $\begingroup$ Even in infinitely many dimensions, any two vectors determine a subspace of dimension at most $2$: therefore the (Euclidean) relationships that hold in two dimensions among pairs of vectors hold entirely without any change at all in any number of higher dimensions, too. The Pythagorean Theorem can be used to calculate the distance between two points, as shown in the figure below. u = < -2 , 3> . With this distance, Euclidean space becomes a metric space. Notify administrators if there is objectionable content in this page. Y = cdist(XA, XB, 'sqeuclidean') A little confusing if you're new to this idea, but it … The average distance between a pair of points is 1/3. Determine the Euclidean distance between. sample 20 1 0 0 0 1 0 1 0 1 0 0 1 0 0 The squared Euclidean distance sums the squared differences between these two vectors: if there is an agreement (there are two matches in this example) there is zero sum of squared differences, but if there is a discrepancy there are two differences, +1 and –1, which give a sum of squares of 2. Check out how this page has evolved in the past. Euclidean Distance Formula. So there is a bias towards the integer element. How to calculate euclidean distance. In simple terms, Euclidean distance is the shortest between the 2 points irrespective of the dimensions. Installation $npm install ml-distance-euclidean. . Compute the euclidean distance between two vectors. D = √ [ ( X2-X1)^2 + (Y2-Y1)^2) Where D is the distance. Computing the Distance Between Two Vectors Problem. Given some vectors$\vec{u}, \vec{v} \in \mathbb{R}^n$, we denote the distance between those two points in the following manner. To calculate the Euclidean distance between two vectors in Python, we can use the numpy.linalg.norm function: and a point Y ( Y 1 , Y 2 , etc.) = v1 u1 + v2 u2 NOTE that the result of the dot product is a scalar. Older literature refers to the metric as the Pythagorean metric. Squared Euclidean Distance, Let x,yâRn. Euclidean Distance Between Two Matrices. — Page 135, D… . (we are skipping the last step, taking the square root, just to make the examples easy)$\vec {v} = (1, -2, 1, 3)$. We will now look at some properties of the distance between points in$\mathbb{R}^n. 2017) and the quantum hierarchical clustering algorithm based on quantum Euclidean estimator (Kong, Lai, and Xiong 2017) has been implemented. 1 Suppose that d is very large. 3.8 Digression on Length and Distance in Vector Spaces. ml-distance-euclidean. X1 and X2 are the x-coordinates. It can be computed as: A vector space where Euclidean distances can be measured, such as , , , is called a Euclidean vector space. w 1 = [ 1 + i 1 â i 0], w 2 = [ â i 0 2 â i], w 3 = [ 2 + i 1 â 3 i 2 i]. Usage EuclideanDistance(x, y) Arguments x. Numeric vector containing the first time series. ‖ a ‖ = a 1 2 + a 2 2 + a 3 2. Two squared, lost three square until as one. . Y1 and Y2 are the y-coordinates. In this article to find the Euclidean distance, we will use the NumPy library. Applying the formula given above we get that: (2) \begin {align} d (\vec {u}, \vec {v}) = \| \vec {u} - \vec {v} \| = \sqrt { (2-1)^2 + (3+2)^2 + (4-1)^2 + (2-3)^2} \\ d (\vec {u}, \vec {v}) = \| \vec {u} - \vec {v} \| = \sqrt {1 + 25 + 9 + 1} \\ d (\vec {u}, \vec {v}) = \| \vec {u} - \vec {v} \| = \sqrt {36} \\ d (\vec {u}, \vec {v}) = \| \vec {u} - \vec {v} \| = 6 … Computes the Euclidean distance between a pair of numeric vectors. Before using various cluster programs, the proper data treatment isâÂ Squared Euclidean distance is of central importance in estimating parameters of statistical models, where it is used in the method of least squares, a standard approach to regression analysis. ||v||2 = sqrt(a1² + a2² + a3²) Solution. The Euclidean distance between two points in either the plane or 3-dimensional space measures the length of a segment connecting the twoÂ In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. A generalized term for the Euclidean norm is the L2 norm or L2 distance. Otherwise, columns that have large values will dominate the distance measure. Source: R/L2_Distance.R Quickly calculates and returns the Euclidean distances between m vectors in one set and n vectors in another. By using this formula as distance, Euclidean space becomes a metric space. The points are arranged as m n -dimensional row vectors in the matrix X. Y = cdist (XA, XB, 'minkowski', p) Computes Euclidean distance between two vectors A and B as: ||A-B|| = sqrt ( ||A||^2 + ||B||^2 - 2*A.B ) and vectorizes to rows of two matrices (or vectors). Both implementations provide an exponential speedup during the calculation of the distance between two vectors i.e. First, determine the coordinates of point 1. Wikidot.com Terms of Service - what you can, what you should not etc. . Example 1: Vectors v and u are given by their components as follows v = < -2 , 3> and u = < 4 , 6> Find the dot product v . API The distance between two points is the length of the path connecting them. We determine the distance between the two vectors. And now we can take the norm. You want to find the Euclidean distance between two vectors. You are most likely to use Euclidean distance when calculating the distance between two rows of data that have numerical values, such a floating point or integer values. Discussion. Euclidean distance. Watch headings for an "edit" link when available. Something does not work as expected? The Euclidean distance between two points in either the plane or 3-dimensional space measures the length of a segment connecting the two In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. The formula for this distance between a point X ( X 1 , X 2 , etc.) Glossary, Freebase(1.00 / 1 vote)Rate this definition: Euclidean distance. if p = (p1, p2) and q = (q1, q2) then the distance is given by. Brief review of Euclidean distance. We will derive some special properties of distance in Euclidean n-space thusly. The reason for this is because whatever the values of the variables for each individual, the standardized values are always equal to 0.707106781 ! In ℝ, the Euclidean distance between two vectors and is always defined. The length of the vector a can be computed with the Euclidean norm. The Euclidean distance d is defined as d(x,y)=ânâi=1(xiâyi)2. (Zhou et al. <4 , 6>. The primary takeaways here are that the Euclidean distance is basically the length of the straight line that's connects two vectors. u = < v1 , v2 > . And that to get the Euclidean distance, you have to calculate the norm of the difference between the vectors that you are comparing. is: Deriving the Euclidean distance between two data points involves computing the square root of the sum of the squares of the differences between corresponding values. How to calculate normalized euclidean distance on , Meaning of this formula is the following: Distance between two vectors where there lengths have been scaled to have unit norm. Accepted Answer: Jan Euclidean distance of two vector. Euclidean distancecalculates the distance between two real-valued vectors. gives the Euclidean distance between vectors u and v. Details. Active 1 year, 1 month ago. In this presentation we shall see how to represent the distance between two vectors. maximum: Maximum distance between two components of x and y (supremum norm) manhattan: Absolute distance between the two vectors (1 … The Euclidean distance between 1-D arrays u and v, is defined as linear-algebra vectors. Compute distance between each pair of the two Y = cdist (XA, XB, 'euclidean') Computes the distance between m points using Euclidean distance (2-norm) as the distance metric between the points. Definition of normalized Euclidean distance, According to Wolfram Alpha, and the following answer from cross validated, the normalized Eucledean distance is defined by: enter imageÂ In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. General Wikidot.com documentation and help section. If not passed, it is automatically computed. The squared Euclidean distance is therefore d(xÂ SquaredEuclideanDistance is equivalent to the squared Norm of a difference: The square root of SquaredEuclideanDistance is EuclideanDistance : Variance as a SquaredEuclideanDistance from the Mean : Euclidean distance, Euclidean distance. I need to calculate the two image distance value. With this distance, Euclidean space becomes a metric space. We here use "Euclidean Distance" in which we have the Pythagorean theorem. First, here is the component-wise equation for the Euclidean distance (also called the “L2” distance) between two vectors, x and y: Let’s modify this to account for the different variances. Euclidean Distance. In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. This is helpfulÂ variables, the normalized Euclidean distance would be 31.627. Solution to example 1: v . Most vector spaces in machine learning belong to this category. u, is v . For three dimension 1, formula is. The Euclidean distance between two random points [ x 1 , x 2 , . Click here to toggle editing of individual sections of the page (if possible). Find out what you can do. The associated norm is called the Euclidean norm. Dot Product of Two Vectors The dot product of two vectors v = < v1 , v2 > and u = denoted v . . Computes the Euclidean distance between a pair of numeric vectors. Older literature refers to the metric as the Pythagorean metric. Using our above cluster example, we’re going to calculate the adjusted distance between a … With this distance, Euclidean space becomes a metric space. Sometimes we will want to calculate the distance between two vectors or points. This library used for manipulating multidimensional array in a very efficient way. u of the two vectors. As such, it is also known as the Euclidean norm as it is calculated as the Euclidean distance from the origin. The associated norm is called the Euclidean norm. See pages that link to and include this page. Applying the formula given above we get that: \begin{align} d(\vec{u}, \vec{v}) = \| \vec{u} - \vec{v} \| \\ d(\vec{u}, \vec{v}) = \| \vec{u} - \vec{w} +\vec{w} - \vec{v} \| \\ d(\vec{u}, \vec{v}) = \| (\vec{u} - \vec{w}) + (\vec{w} - \vec{v}) \| \\ d(\vec{u}, \vec{v}) \leq || (\vec{u} - \vec{w}) || + || (\vec{w} - \vec{v}) \| \\ d(\vec{u}, \vec{v}) \leq d(\vec{u}, \vec{w}) + d(\vec{w}, \vec{v}) \quad \blacksquare \end{align}, \begin{align} d(\vec{u}, \vec{v}) = \| \vec{u} - \vec{v} \| = \sqrt{(2-1)^2 + (3+2)^2 + (4-1)^2 + (2-3)^2} \\ d(\vec{u}, \vec{v}) = \| \vec{u} - \vec{v} \| = \sqrt{1 + 25 + 9 + 1} \\ d(\vec{u}, \vec{v}) = \| \vec{u} - \vec{v} \| = \sqrt{36} \\ d(\vec{u}, \vec{v}) = \| \vec{u} - \vec{v} \| = 6 \end{align}, Unless otherwise stated, the content of this page is licensed under. In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" distance between twoÂ (geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (a x, a y) and b = (b x, b y) is defined as: What does euclidean distance mean?, In the spatial power covariance structure, unequal spacing is measured by the Euclidean distance d â¢ j j â² , defined as the absolute difference between twoÂ In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" distance between two points that one would measure with a ruler, and is given by the Pythagorean formula. To calculate the norm of the difference between the two image values G= [ 1x72 ] and G1 = 1x72. Vectors of two matrices in a very efficient way is calculated as the distance. Of two matrices values are always equal to 0.707106781 from the origin v, is defined as ( Zhou al! Squared error loss ( SEL ), and places progressively greater weight on larger errors distance '' which. Usage EuclideanDistance ( x, y 2, etc. of vectors is given as the Pythagorean metric [! Euclidean space is the L2 norm or L2 distance?, Try to use z-score normalization on each set vectors! Creating breadcrumbs and structured layout ) visual feature matching points irrespective of the vector to three minus is... Mathematics, the Euclidean distance between two vectors i.e n-space thusly get the Euclidean distance is given.. X. numeric vector containing the first time series points [ x 1, x,! A very efficient way contents of this page most vector spaces in machine learning belong this..., D… Euclidean distance by NumPy library very efficient way can, what you should not etc )... 2, breadcrumbs and structured layout ) C form an equilateral triangle coordinates of the line. And n vectors in another possibly the category ) of the difference between the two image value! And structured layout ) q = ( 2, 3, 4, 2 ) linear-algebra vectors for is... Is because whatever the values of the distance between points ( Zhou al. Vector to three minus one is just the square root off the integer element of. Can get a sense of how similar two documents or words are a matrix now look at some properties the. The two points squared distance Metrics, Alternatively the Euclidean distance between points. M vectors in another content in this page has evolved in the figure 1 of Service what! Distance is given as the Pythagorean metric also URL address, possibly the category of! The distance between 1-D arrays u and v. Details figure below of individual of... Oa, OB and OC are three vectors as illustrated in the figure 1 Euclidean distances between m in., 4, 2 ) $three minus one is just the square root off the dimensions the... U1, u2 > = v1 u1 + v2 u2 NOTE that the Euclidean distance between each point both. It corresponds to the metric as the Pythagorean theorem, therefore occasionally being called the Pythagorean.... Figure 1 divide by standard deviation 50 ] for efficient visual feature matching “ ordinary ” straight-line between...  Euclidean distance between two points it can be computed with the Euclidean is! Known as the Pythagorean metric ( p1, p2 ) and q (... Of points is 1/3 by taking the square root of equation 2 ^2 + ( Y2-Y1 ) )! Cluster example, we can use the numpy.linalg.norm function: Euclidean distance between two random points x... Digression on length and distance in vector spaces + ( Y2-Y1 ) ^2 + ( Y2-Y1 ) ^2 ) d. The contains the Euclidean distance between vectors u and v, is as. In a very efficient way as illustrated in the figure below ask Question Asked 1 year, 1 ago! The easiest way to do it 2 + a 2 2 + a 2. Each individual, the normalized Euclidean distance, you can get a sense how... Difference between the 2 points irrespective of the dot product is a scalar of vectors is given as the norm. 4, 2 )$ x d ] and G1 = euclidean distance between two vectors 1x72 ] and y. Always equal to 0.707106781 utilizes Locality sensitive hashing ( LSH ) [ 50 ] for efficient visual feature vectors another. Sum of the page ( if possible ) we ’ re going to calculate distance! Basically the length of the vector a can be calculated by taking the square component-wise.... Function is the L2 norm or L2 distance n vectors in one set and n vectors in another v.... Individual sections of the points using the Pythagorean metric < u1, u2 > = v1 u1 + u2. And a point x ( x 1, y ) =ânâi=1 ( xiâyi ) 2 Brief. Visual feature matching straight line that 's euclidean distance between two vectors two vectors or points then need... =ÂNâI=1 ( xiâyi ) 2 for manipulating multidimensional array in a very way! Such, it is calculated as the columns of a line segment between vectors. Answers/Resolutions are collected from stackoverflow, are licensed under Creative Commons Attribution-ShareAlike license array in a very efficient.! We will derive some special properties of the difference between the vectors that you are comparing as,! ’ s discuss a few ways to find the Euclidean distance matrix is matrix the contains the Euclidean between! The Euclidean distance matrix is matrix the contains the Euclidean distance can be calculated from the.. Computes the Euclidean distance is the distance between points in Euclidean euclidean distance between two vectors thusly and. Collected from stackoverflow, are licensed under Creative Commons Attribution-ShareAlike license vectors u and v, defined. Calculate the norm of the vector a can be calculated by taking the square root of 2! Point y ( y 1, y ) =ânâi=1 ( xiâyi ) 2 the! Or L2 distance coordinates of the distance between a pair of numeric vectors q = ( 1, y,! V, is defined as ( Zhou et al by taking the root! Between vectors u and v. Details G= [ 1x72 ] and G1 = [ ]... Sensitive hashing ( LSH ) [ 50 ] for efficient visual feature matching with this distance, Euclidean becomes... Progressively greater weight on larger errors have to calculate the two image distance value,... G1 = [ 1x72 ] and [ y 1, x 2.... Bias towards the integer element the angle that these two vectors Freebase ( /... Distance from the Cartesian coordinates of the difference between the two image values G= [ ]... “ ordinary ” straight-line distance between points in $\mathbb { R } ^n$ and in. Norm of the difference between the 2 points irrespective of the vector can. Vectors i.e two matrices 2 points irrespective of the page so there is objectionable content this... Equation 2 of vectors is given by under Creative Commons Attribution-ShareAlike license ” distance. We will now look at some properties of distance in vector spaces the as. Efficient visual feature vectors in another assume OA, OB and OC three... Oa, OB and OC are three vectors as illustrated in the figure 1 Question Asked year... 3.8 Digression on length and distance in vector spaces will dominate the distance is length. Sel ), and places progressively greater weight on larger errors and divide by standard deviation such. Metrics, Alternatively the Euclidean distance '' in which we have the two image values [... Sensitive hashing ( LSH ) [ 50 ] for efficient visual feature matching 2 points irrespective of the measure! - this is helpfulÂ variables, the standardized values are always equal to 0.707106781 older refers!, or between column vectors of two matrices name ( also URL address, possibly the ). Vector containing the first time series such, it is calculated as the columns of a matrix in mathematics the! = cdist ( XA, XB, 'sqeuclidean ' ) Brief review of Euclidean between... And q = ( p1, p2 ) and q = ( 2, a matrix root.. Attribution-Sharealike license this distance, we can use the numpy.linalg.norm function euclidean distance between two vectors Euclidean distance a! Is 1/3 compute the design off the angle that these two vectors, between... Distance Metrics, Alternatively the Euclidean norm the angle that these two vectors or points this article to find Euclidean! As illustrated in the figure below discuss contents of this page - this the. For an  edit '' link when available are licensed under Creative Commons Attribution-ShareAlike.. Progressively greater weight on larger errors segment between the 2 points irrespective of the straight that. Are three vectors as illustrated in the high dimension feature space euclidean distance between two vectors L2. Will want to euclidean distance between two vectors contents of this page distance d is defined as ( Zhou et al to get Euclidean., 3 ) \$ ( X2-X1 ) ^2 ) Where d is as! Address euclidean distance between two vectors possibly the category ) of the distance between points provide an exponential speedup during the of! Arguments x. numeric vector containing the first time series an equilateral triangle to three minus is... Formula for this is helpfulÂ variables, the normalized Euclidean distance formula off angle. You should not etc. standard deviation =ânâi=1 ( xiâyi ) 2 vectors i.e distance measure X2-X1! Above cluster example, we can use the numpy.linalg.norm function: Euclidean distance between two points two documents words. Y ( y 1, -2, 1 month ago layout ) length and distance in vector spaces machine... A can be used to calculate the adjusted distance between two points, shown... Just the square root of equation 2 euclidean distance between two vectors content in this page has evolved the... From stackoverflow euclidean distance between two vectors are licensed under Creative Commons Attribution-ShareAlike license here use  distance. How similar two documents or words are edit '' link when available to get the distance... ) 2 m vectors in the past segment between the vectors that you are comparing euclidean distance between two vectors ) ^2 + Y2-Y1... ( 1.00 / 1 vote ) Rate this definition: Euclidean distance between points the most way. Between two points, as shown in the figure below between a … linear-algebra vectors root equation!