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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.

The characteristic polynomial is the polynomial left-hand side of the characteristic equation det(A-lambdaI)=0, (1) where A is a square matrix and I is the identity matrix of ...

The power series that defines the exponential map e^x also defines a map between matrices. In particular, exp(A) = e^(A) (1) = sum_(n=0)^(infty)(A^n)/(n!) (2) = ...

A unimodular matrix is a real square matrix A with determinant det(A)=+/-1 (Born and Wolf 1980, p. 55; Goldstein 1980, p. 149). More generally, a matrix A with elements in ...

The idiosyncratic polynomial is the bivariate graph polynomial defined as the characteristic polynomial in x of A+y(J-I-A), where A is the adjacency matrix, J is the unit ...

A Vandermonde matrix is a type of matrix that arises in the polynomial least squares fitting, Lagrange interpolating polynomials (Hoffman and Kunze p. 114), and 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 ...

If the Tutte polynomial T(x,y) of a graph G is given by sumt_(rs)x^ry^s, then the matrix (t_(rs)) is called the rank matrix of G. For example, the Tutte matrix of the ...

A positive matrix is a real or integer matrix (a)_(ij) for which each matrix element is a positive number, i.e., a_(ij)>0 for all i, j. Positive matrices are therefore a ...

The Laplacian matrix, sometimes also called the admittance matrix (Cvetković et al. 1998, Babić et al. 2002) or Kirchhoff matrix, of a graph G, where G=(V,E) is an ...