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A square matrix A such that A^2=I, where I is the identity matrix. An involutory matrix is its own matrix inverse.

Let X={x_1>=x_2>=...>=x_n|x_i in R} (1) and Y={y_1>=y_2>=...>=y_n|y_i in R}. (2) Then there exists an n×n Hermitian matrix with eigenvalues X and diagonal elements Y iff ...

A polynomial with matrix coefficients. An nth order matrix polynomial in a variable t is given by P(t)=A_0+A_1t+A_2t^2+...+A_nt^n, where A_k are p×p square matrices.

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

A series-reduced tree is a tree in which all nodes have degree other than 2 (in other words, no node merely allows a single edge to "pass through"). Series-reduced trees are ...

A weakly binary tree is a planted tree in which all nonroot graph vertices are adjacent to at most three graph vertices. Let g(z)=sum_(i=0)^inftyg_iz^i, (1) be the generating ...

The Gershgorin circle theorem (where "Gershgorin" is sometimes also spelled "Gersgorin" or "Gerschgorin") identifies a region in the complex plane that contains all the ...

The detour matrix Delta, sometimes also called the maximum path matrix or maximal topological distances matrix, of a graph is a symmetric matrix whose (i,j)th entry is the ...

A theorem due to Conway et al. (1997) which states that, if a positive definite quadratic form with integer matrix entries represents all natural numbers up to 15, then it ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...