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The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

A periodic matrix with period 1, so that A^2=A.

The rank of a matrix or a linear transformation is the dimension of the image of the matrix or the linear transformation, corresponding to the number of linearly independent ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

An n×n-matrix A is said to be diagonalizable if it can be written on the form A=PDP^(-1), where D is a diagonal n×n matrix with the eigenvalues of A as its entries and P is a ...

A stochastic matrix, also called a probability matrix, probability transition matrix, transition matrix, substitution matrix, or Markov matrix, is matrix used to characterize ...

A group in which the elements are square matrices, the group multiplication law is matrix multiplication, and the group inverse is simply the matrix inverse. Every matrix ...

A real matrix is a matrix whose elements consist entirely of real numbers. The set of m×n real matrices is sometimes denoted R^(m×n) (Zwillinger 1995, p. 116).

Any discrete finite wavelet transform can be represented as a matrix, and such a wavelet matrix can be computed in O(n) steps, compared to O(nlgn) for the Fourier matrix, ...

An Alexander matrix is a presentation matrix for the Alexander invariant H_1(X^~) of a knot K. If V is a Seifert matrix for a tame knot K in S^3, then V^(T)-tV and V-tV^(T) ...