invertible matrix

The case of a square invertible matrix also holds interest.

Furthermore, the following properties hold for an invertible matrix A:

Notice that the polar decomposition of an invertible matrix is unique.

Since only invertible matrices can be used for the key, the effective key size is about 4094.2 bits.

Note that the exponential of a matrix is always an invertible matrix.

Not all matrices have an inverse (see invertible matrix).

The number of invertible matrices modulo 26 is the product of those two numbers.

The elementary matrices generate the general linear group of invertible matrices.

For example the general linear group of 2x2 real invertible matrices has a transitive action on it.

Finite groups are collections of invertible matrices that are applied to a variable.

See invertible matrix for more.

Suppose that the invertible matrix 'A' depends on a parameter 't'.

The number of invertible matrices can be computed via the Chinese Remainder Theorem.

In addition to providing a computational tool, this formula demonstrates that a matrix exponential is always an invertible matrix.

If a square, invertible matrix has an LDU factorization, then it is unique.

For this, the code's generator matrix is perturbated by two randomly selected invertible matrices and (see below).

Since the above matrix has a nonzero determinant, its columns form a basis of R. See: invertible matrix.

Let be a prime number such that divides , and let be an invertible matrix over to be chosen later.

One can write down the inverse of an invertible matrix by computing its cofactors by using Cramer's rule, as follows.

The collection of all such invertible matrices constitutes the general linear group GL(2, R).

Multiplication by the invertible matrix maps a uniformly chosen to a uniformly chosen .

Matrices over such a ring can be put in Hermite normal form by right multiplication by a square invertible matrix (, p. 468.)

Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.

Furthermore the n-by-n invertible matrices are a dense open set in the topological space of all n-by-n matrices.

Only invertible row and column operations are performed, which ensures that S and T remain invertible matrices.