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The four parameters e_0, e_1, e_2, and e_3 describing a finite rotation about an arbitrary axis. The Euler parameters are defined by e_0 = cos(phi/2) (1) e = [e_1; e_2; e_3] ...

A univariate distribution proportional to the F-distribution. If the vector d is Gaussian multivariate-distributed with zero mean and unit covariance matrix N_p(0,I) and M is ...

A generalized eigenvector for an n×n matrix A is a vector v for which (A-lambdaI)^kv=0 for some positive integer k in Z^+. Here, I denotes the n×n identity matrix. The ...

The polynomials in the diagonal of the Smith normal form or rational canonical form of a matrix are called its invariant factors.

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.

There are two types of singular values, one in the context of elliptic integrals, and the other in linear algebra. For a square matrix A, the square roots of the eigenvalues ...

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 ...

An n-Hadamard graph is a graph on 4n vertices defined in terms of a Hadamard matrix H_n=(h)_(ij) as follows. Define 4n symbols r_i^+, r_i^-, c_i^+, and c_i^-, where r stands ...

The matrix operations of 1. Interchanging two rows or columns, 2. Adding a multiple of one row or column to another, 3. Multiplying any row or column by a nonzero element.

Let A = [B D; E C] (1) A^(-1) = [W X; Y Z], (2) where B and W are k×k matrices. Then det(Z)det(A)=det(B). (3) The proof follows from equating determinants on the two sides of ...