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The matrix decomposition of a square matrix A into so-called eigenvalues and eigenvectors is an extremely important one. This decomposition generally goes under the name ...

The Hilbert-Schmidt norm of a matrix A is a matrix norm defined by ||A||_(HS)=sqrt(sum_(i,j)a_(ij)^2).

The generalized Gell-Mann matrices are the n^2-1 matrices generating the Lie algebra associated to the special unitary group SU(n), n>=2. As their name suggests, these ...

The numerators and denominators obtained by taking the ratios of adjacent terms in the triangular array of the number of +1 "bordered" alternating sign matrices A_n with a 1 ...

The Kronecker sum is the matrix sum defined by A direct sum B=A tensor I_b+I_a tensor B, (1) where A and B are square matrices of order a and b, respectively, I_n is the ...

A p×q submatrix of an m×n matrix (with p<=m, q<=n) is a p×q matrix formed by taking a block of the entries of this size from the original matrix.

The superdiagonal of a square matrix is the set of elements directly above the elements comprising the diagonal. For example, in the following matrix, the diagonal elements ...

To solve the system of differential equations (dx)/(dt)=Ax(t)+p(t), (1) where A is a matrix and x and p are vectors, first consider the homogeneous case with p=0. The ...

If a matrix group is reducible, then it is completely reducible, i.e., if the matrix group is equivalent to the matrix group in which every matrix has the reduced form ...

A square matrix A is said to be unipotent if A-I, where I is an identity matrix is a nilpotent matrix (defined by the property that A^n is the zero matrix for some positive ...