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Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...

A matrix, also called a canonical box matrix, having zeros everywhere except along the diagonal and superdiagonal, with each element of the diagonal consisting of a single ...

The quotient space K^__1A=K_1A/{0,[-1]} of the Whitehead group K_1A is known as the reduced Whitehead group. Here, the element [-1] in K_1A denotes the order-2 element ...

A square matrix that is not singular, i.e., one that has a matrix inverse. Nonsingular matrices are sometimes also called regular matrices. A square matrix is nonsingular iff ...

An orthonormal set is a set of normalized orthogonal vectors or functions.

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.

If W is a k-dimensional subspace of a vector space V with inner product <,>, then it is possible to project vectors from V to W. The most familiar projection is when W is the ...

The subdiagonal of a square matrix is the set of elements directly under the elements comprising the diagonal. For example, in the following matrix, the diagonal elements are ...

The bandwidth of a matrix M=(m_(ij)) is the maximum value of |i-j| such that m_(ij) is nonzero.

A matrix whose eigenvectors are not complete.