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The trace of an n×n square matrix A is defined to be Tr(A)=sum_(i=1)^na_(ii), (1) i.e., the sum of the diagonal elements. The matrix trace is implemented in the Wolfram ...

Hadamard's maximum determinant problem asks to find the largest possible determinant (in absolute value) for any n×n matrix whose elements are taken from some set. Hadamard ...

A (-1,0,1)-matrix is a matrix whose elements consist only of the numbers -1, 0, or 1. The number of distinct (-1,0,1)-n×n matrices (counting row and column permutations, the ...

A C-matrix is a symmetric (C^(T)=C) or antisymmetric (C^(T)=-C) C_n (-1,0,1)-matrix with diagonal elements 0 and others +/-1 that satisfies CC^(T)=(n-1)I, (1) where I is the ...

The Cayley-Menger determinant is a determinant that gives the volume of a simplex in j dimensions. If S is a j-simplex in R^n with vertices v_1,...,v_(j+1) and B=(beta_(ik)) ...

An n×n matrix whose rows are composed of cyclically shifted versions of a length-n list l. For example, the 4×4 circulant matrix on the list l={1,2,3,4} is given by C=[4 1 2 ...

A method of computing the determinant of a square matrix due to Charles Dodgson (1866) (who is more famous under his pseudonym Lewis Carroll). The method is useful for hand ...

A diagonal matrix is a square matrix A of the form a_(ij)=c_idelta_(ij), (1) where delta_(ij) is the Kronecker delta, c_i are constants, and i,j=1, 2, ..., n, with no implied ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

A square matrix is called Hermitian if it is self-adjoint. Therefore, a Hermitian matrix A=(a_(ij)) is defined as one for which A=A^(H), (1) where A^(H) denotes the conjugate ...