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A unimodular matrix is a real square matrix A with determinant det(A)=+/-1 (Born and Wolf 1980, p. 55; Goldstein 1980, p. 149). More generally, a matrix A with elements in ...

A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies det(A)=+/-1. A necessary and sufficient condition that a linear transformation transform a ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

A left Hilbert Algebra A whose involution is an antilinear isometry is called a unimodular Hilbert algebra. The involution is usually denoted xi|->xi^*.

A unit matrix is an integer matrix consisting of all 1s. The m×n unit matrix is often denoted J_(mn), or J_n if m=n. Square unit matrices J_n have determinant 0 for n>=2. An ...

A group whose left Haar measure equals its right Haar measure.

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; ...

A matrix for which horizontal and vertical dimensions are not the same (i.e., an m×n matrix with m!=n).

A square matrix A such that A^2=I, where I is the identity matrix. An involutory matrix is its own matrix inverse.

A positive matrix is a real or integer matrix (a)_(ij) for which each matrix element is a positive number, i.e., a_(ij)>0 for all i, j. Positive matrices are therefore a ...