Within mathematics, an N×NEuclidean random matrix  is defined with the help of an arbitrary deterministic function f(r, r′) and of N points {ri} randomly distributed in a region V of d-dimensional Euclidean space. The element Aij of the matrix is equal to f(ri, rj): Aij = f(ri, rj).
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mathematics, an N×N Euclideanrandommatrix  is defined with the help of an arbitrary deterministic function f(r, r′) and of N points {ri} randomly distributed...
In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space. For points x 1 , x 2 ,...
mathematics and statistics, random projection is a technique used to reduce the dimensionality of a set of points which lie in Euclidean space. According to theoretical...
where Q is an orthogonal matrix. To see the inner product connection, consider a vector v in an n-dimensional real Euclidean space. Written with respect...
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements...
covariance matrix is called the precision matrix, denoted by Q = Σ − 1 {\displaystyle {\boldsymbol {Q}}={\boldsymbol {\Sigma }}^{-1}} . A real random vector...
rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [...
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers...
to as a pre-distance matrix. A pre-distance matrix that can be embedded in a Euclidean space is called a Euclidean distance matrix. For mixed-type data...
with the usual Euclidean dot product, the Gram matrix is G = V ⊤ V {\displaystyle G=V^{\top }V} , where V {\displaystyle V} is a matrix whose columns are...
25 {\displaystyle (33+\varepsilon )/25} by a randomized algorithm. The TSP, in particular the Euclidean variant of the problem, has attracted the attention...
a square matrix's entries are randomly selected from any bounded region on the number line or complex plane, the probability that the matrix is singular...
columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number...
In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function...
plane or some higher-dimensional Euclidean space, then the collection of random variables is usually called a random field instead. The values of a stochastic...
( X − μ ) 2 {\displaystyle (X-\mu )^{2}} as the squared Euclidean distance between the random variable and its mean, or, simply as the scalar product...
information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models...
transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they...
{\displaystyle n} -dimensional Euclidean space, with the singular values of any n × n {\displaystyle n\times n} square matrix being viewed as the magnitude...
In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical...
vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial...
is half of the squared Euclidean distance of the L 2 {\displaystyle L_{2}} normalization of the vectors, and squared Euclidean distance does not satisfy...
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various...
are very small, so a fair number of steps of the Euclidean algorithm can be collected in a 2-by-2 matrix of single-word integers. When Lehmer's algorithm...
distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f ( x...
unit variance, then the Mahalanobis distance corresponds to standard Euclidean distance in the transformed space. The Mahalanobis distance is thus unitless...
study of non-symmetric random matrices. They showed that if n is large and the entries of a n × n matrix A are selected randomly according to any fixed...
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