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Although an explicit inverse is not necessary to estimate the vector of unknowns, it is the easiest way to estimate their accuracy, found in the diagonal of a matrix inverse (the posterior covariance matrix of the vector of unknowns). However, faster algorithms to compute only the diagonal entries of a matrix inverse are known in many cases. [19]
In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns. Minors obtained by removing just one row and one column from square matrices (first minors) are required for calculating matrix cofactors, which are useful for computing both the determinant and inverse of square matrices.
Cofactor may also refer to: Cofactor (biochemistry), a substance that needs to be present in addition to an enzyme for a certain reaction to be catalysed; A domain parameter in elliptic curve cryptography, defined as the ratio between the order of a group and that of the subgroup; Cofactor (linear algebra), the signed minor of a matrix
In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. [1] [2] It is occasionally known as adjunct matrix, [3] [4] or "adjoint", [5] though that normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose.
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]
This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse: =, where Q −1 is the inverse of Q. An orthogonal matrix Q is necessarily invertible (with inverse Q −1 = Q T), unitary (Q −1 = Q ∗), where Q ∗ is the Hermitian adjoint (conjugate transpose) of Q, and therefore normal (Q ...
A cofactor is a non-protein chemical compound or metallic ion that is required for an enzyme's role as a catalyst (a catalyst is a substance that increases the rate of a chemical reaction). Cofactors can be considered "helper molecules" that assist in biochemical transformations.
Reciprocal polynomials arise naturally in linear algebra as the characteristic polynomial of the inverse of a matrix. In the special case where the field is the complex numbers, when = + + + +, the conjugate reciprocal polynomial, denoted p †, is defined by,