inverse to undo the operation. An invertible matrix multiplied by its inverse yields the identity matrix. Invertible matrices are the same size as their...

general linear group of all invertible matrices. A triangular matrix is invertible precisely when its diagonal entries are invertible (non-zero). Over the real...

invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with the identity matrix as the identity element of the...

,} where I is the identity matrix of the same size as A. Consequently, the multiplicative inverse of an invertible matrix can be found by dividing its...

matrix A {\displaystyle A}  is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists an invertible matrix...

an invertible element is an element that has an inverse. In a ring, an invertible element, also called a unit, is an element that is invertible under...

A matrix is positive semi-definite if it satisfies similar equivalent conditions where "positive" is replaced by "nonnegative", "invertible matrix" is...

defined using the Leibniz formula; such a matrix is invertible if and only if its determinant is invertible in R, generalizing the situation over a field...

m\times n} matrix A {\displaystyle A} . A square matrix A {\displaystyle A} is called invertible or non-singular if there exists a matrix B {\displaystyle...

identity matrix. Involutory matrices are all square roots of the identity matrix. This is a consequence of the fact that any invertible matrix multiplied...

{T} }=Q^{-1},} where Q−1 is the inverse of Q. An orthogonal matrix Q is necessarily invertible (with inverse Q−1 = QT), unitary (Q−1 = Q∗), where Q∗ is the...

in particular linear algebra, the matrix determinant lemma computes the determinant of the sum of an invertible matrix A and the dyadic product, u vT, of...

Invertible may refer to Invertible element Invertible function Invertible ideal Invertible knot Invertible jet Invertible matrix Invertible module Invertible...

inverse of a "rank-1 update" to a matrix whose inverse has previously been computed. That is, given an invertible matrix A {\displaystyle A} and the outer...

of a Lie algebra, when the Lie algebra is gln Invertible matrix (this usage is rare) QS Regular Matrix, a quadraphonic sound system developed by Sansui...

represented, on a given basis, by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the corresponding linear map...

given number yields the multiplicative identity, 1 Inverse matrix of an Invertible matrix Invert level, the base interior level of a pipe, trench or tunnel...

the left by an n × n invertible matrix S, and the symmetric square matrix A is transformed into another symmetric square matrix B of the same size according...

In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U−1 equals its conjugate transpose U*, that is, if U ∗ U = U...

congruent if there exists an invertible matrix P over the same field such that PTAP = B where "T" denotes the matrix transpose. Matrix congruence is an equivalence...

{2}}\end{bmatrix}}.} An invertible matrix A is a generalized permutation matrix if and only if it can be written as a product of an invertible diagonal matrix D and an...

The transpose of an invertible matrix is also invertible, and its inverse is the transpose of the inverse of the original matrix. The notation A−T is...

the inverse of an invertible matrix. The method is named after Carl Friedrich Gauss (1777–1855). To perform row reduction on a matrix, one uses a sequence...

invertible matrices. In fact, this map is surjective which means that every invertible matrix can be written as the exponential of some other matrix (for...

=\mathbf {I} .} A matrix that has an inverse is an invertible matrix. Otherwise, it is a singular matrix. A product of matrices is invertible if and only if...

diagonal matrix is invertible if and only if each of its main-diagonal blocks are invertible, and in this case its inverse is another block diagonal matrix given...

words, the matrix of the combined transformation A followed by B is simply the product of the individual matrices. When A is an invertible matrix there is...

a unimodular matrix M is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers:...

\dots ,\ x_{n}} are distinct, then V is a square matrix with non-zero determinant, i.e. an invertible matrix. Thus, given V and y, one can find the required...

transformation is invertible, the square matrix A {\displaystyle A} appearing in its matrix representation is invertible. The matrix representation of...