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A square matrix A is a normal matrix if [A,A^(H)]=AA^(H)-A^(H)A=0, where [a,b] is the commutator and A^(H) denotes the conjugate transpose. For example, the matrix [i 0; 0 ...

A square matrix U is a unitary matrix if U^(H)=U^(-1), (1) where U^(H) denotes the conjugate transpose and U^(-1) is the matrix inverse. For example, A=[2^(-1/2) 2^(-1/2) 0; ...

The eight Gell-Mann matrices lambda_i, i=1,...,8, are an example of the set of generators of the Lie algebra associated to the special unitary group SU(3). Explicitly, these ...

A zero matrix is an m×n matrix consisting of all 0s (MacDuffee 1943, p. 27), denoted 0. Zero matrices are sometimes also known as null matrices (Akivis and Goldberg 1972, p. ...

The matrix direct sum of n matrices constructs a block diagonal matrix from a set of square matrices, i.e., direct sum _(i=1)^nA_i = diag(A_1,A_2,...,A_n) (1) = [A_1 ; A_2 ; ...

Two matrices A and B are said to be equal iff a_(ij)=b_(ij) (1) for all i,j. Therefore, [1 2; 3 4]=[1 2; 3 4], (2) while [1 2; 3 4]!=[0 2; 3 4]. (3)

Proved in 1933. If q is an odd prime or q=0 and n is any positive integer, then there is a Hadamard matrix of order m=2^e(q^n+1), where e is any positive integer such that ...

If the matrices A, X, B, and C satisfy AX-XB=C, then [I X; 0 I][A C; 0 B][I -X; 0 I]=[A 0; 0 B], where I is the identity matrix.

An integer matrix whose entries satisfy a_(ij)={0 if j>i+1; -1 if j=i+1; 0 or 1 if j<=i. (1) There are 2^(n-1) special minimal matrices of size n×n.

The product C of two matrices A and B is defined as c_(ik)=a_(ij)b_(jk), (1) where j is summed over for all possible values of i and k and the notation above uses the ...