Matrix theory

Field of values in matlab

The following Matlab project contains the source code and Matlab examples used for field of values. The Field of values of a matrix is a convex set in the complex plane that contains all eigenvalues of the given matrix, however, it is usually difficult to see the shape of this Field of values; this m-file plots boundary points of this set and the eigenvalues of the given matrix.

Ginv(x) in matlab

The following Matlab project contains the source code and Matlab examples used for ginv(x). Matlab's PINV(X) computes the Moore-Penrose generalized inverse of X, which is unique. Instead, GINV(X) computes any g-inverse of X. In fact, GINV returns a different g-inverse in each draw.

Kronecker tensor product in matlab

The following Matlab project contains the source code and Matlab examples used for kronecker tensor product. Kronecker product of the two matrix arguments in the order they appear If A is an m-by-n matrix and B is a p-by-q matrix, then the Kronecker product is the mp-by-nq block matrix    example, if X is 2 by 3, then KRONECKER(X,Y) is       [ X(1,1)*Y X(1,2)*Y X(1,3)*Y         X(2,1)*Y X(2,2)*Y X(2,3)*Y ] Thanks to Etienne Grossmann & Bruno Luong Mayowa.

Mmtimes matrix chain product in matlab

The following Matlab project contains the source code and Matlab examples used for mmtimes matrix chain product. Because the matrix multiplication is associative; the product can be carried with different order, leading to the same result up to round-off error, MMTIMES usings "optimal" order of binary product to reduce the computational effort (probably accuracy is also improved) The function assumes the cost of the product of (m x n) with (n x p) matrices is (m*n*p).

An implementation of the kronecker product for multidimensional arrays. in matlab

The following Matlab project contains the source code and Matlab examples used for an implementation of the kronecker product for multidimensional arrays. . Superkron is a generalization of Matlab's kron function. It allows to compute the kronecker product of more than two matrices in one shot, and also works for multidimensional arrays having more than two dimensions.

Nonnegative matrix and tensor factorization (nmf, ntf) with any beta divergence in matlab

The following Matlab project contains the source code and Matlab examples used for nonnegative matrix and tensor factorization (nmf, ntf) with any beta divergence. function [W,H,Q, Vhat] = betaNTF(V,K,varargin) %------------------------------------------------------------------ % simple beta-NTF implementation % % Decomposes a tensor V of dimension FxTxI into a NTF model : % V(f,t,i) = \sum_k W(f,k)H(t,k)Q(i,k) % % by minimizing a beta-divergence as a cost-functions.

Matrix polynomial in matlab

The following Matlab project contains the source code and Matlab examples used for matrix polynomial. This is a variation of MATLAB's polyvalm function, with a more efficient implementation. For a polynomial of order p, the number of matrix multiplies is approximately 2*(sqrt(p+1)-1). [See also polyvalm2, File ID: #25780.]

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