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Diffusion maps exploit the relationship between heat diffusion and random walk Markov chain.The basic observation is that if we take a random walk on the data, walking to a nearby data-point is more likely than walking to another that is far away.
The pseudo-Hadamard transform is a reversible transformation of a bit string that provides cryptographic diffusion. See Hadamard transform. The bit string must be of even length so that it can be split into two bit strings a and b of equal lengths, each of n bits.
In mathematics, the Smith normal form (sometimes abbreviated SNF [1]) is a normal form that can be defined for any matrix (not necessarily square) with entries in a principal ideal domain (PID). The Smith normal form of a matrix is diagonal, and can be obtained from the original matrix by multiplying on the left and right by invertible square ...
The probability density function for the random matrix X (n × p) that follows the matrix normal distribution , (,,) has the form: (,,) = ([() ()]) / | | / | | /where denotes trace and M is n × p, U is n × n and V is p × p, and the density is understood as the probability density function with respect to the standard Lebesgue measure in , i.e.: the measure corresponding to integration ...
It is possible to give a fairly long list of equivalent definitions of a normal matrix. Let A be a n × n complex matrix. Then the following are equivalent: A is normal. A is diagonalizable by a unitary matrix. There exists a set of eigenvectors of A which forms an orthonormal basis for C n.
The row echelon form is a canonical form, when one considers as equivalent a matrix and its left product by an invertible matrix. In computer science, and more specifically in computer algebra , when representing mathematical objects in a computer, there are usually many different ways to represent the same object.
A matrix normal form or matrix canonical form describes the transformation of a matrix to another with special properties. Pages in category "Matrix normal forms" The following 10 pages are in this category, out of 10 total.
The Jordan normal form is the most convenient for computation of the matrix functions (though it may be not the best choice for computer computations). Let f(z) be an analytical function of a complex argument. Applying the function on a n×n Jordan block J with eigenvalue λ results in an upper triangular matrix: