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Invertible matrix. In linear algebra, an invertible matrix is a square matrix which has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an inverse to undo the operation. Invertible matrices are the same size as their inverse.
Moore–Penrose inverse. In mathematics, and in particular linear algebra, the Moore–Penrose inverse of a matrix , often called the pseudoinverse, is the most widely known generalization of the inverse matrix. [1] It was independently described by E. H. Moore in 1920, [2] Arne Bjerhammar in 1951, [3] and Roger Penrose in 1955. [4]
A matrix whose elements are of the form 1/ (xi + yj) for (xi), (yj) injective sequences (i.e., taking every value only once). Centrosymmetric matrix. A matrix symmetric about its center; i.e., aij = an−i+1,n−j+1. Circulant matrix. A matrix where each row is a circular shift of its predecessor. Conference matrix.
The manipulations of the Rubik's Cube form the Rubik's Cube group.. In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.
Definition. The transpose of a matrix A, denoted by AT, [3] ⊤A, A⊤, , [4][5] A′, [6] Atr, tA or At, may be constructed by any one of the following methods: Reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain AT. Write the rows of A as the columns of AT.
In mathematics, an involutory matrix is a square matrix that is its own inverse. That is, multiplication by the matrix is an involution if and only if where is the identity matrix. Involutory matrices are all square roots of the identity matrix. This is a consequence of the fact that any invertible matrix multiplied by its inverse is the identity.
Generalized inverse. Algebraic element satisfying some of the criteria of an inverse. In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is ...
The Drazin inverse of a matrix of index 0 or 1 is called the group inverse or {1,2,5}-inverse and denoted A #. The group inverse can be defined, equivalently, by the properties AA # A = A, A # AA # = A #, and AA # = A # A. A projection matrix P, defined as a matrix such that P 2 = P, has index 1 (or 0) and has Drazin inverse P D = P.