Sylvester's determinant theorem
- Sylvester's determinant theorem
In matrix theory, Sylvester's determinant theorem is a theorem useful for evaluating certain types of determinants. It is named after James Joseph Sylvester.
The theorem states that if "A", "B" are matrices of size "p" × "n" and "n" × "p" respectively, then
:
where "I""a" is the identity matrix of order "a".
This theorem is useful in developing a Bayes estimator for multivariate Gaussian distributions.
Sylvester (1857) stated this theorem without proof.
Wikimedia Foundation.
2010.
Look at other dictionaries:
Determinant — This article is about determinants in mathematics. For determinants in epidemiology, see Risk factor. In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific… … Wikipedia
James Joseph Sylvester — Infobox Scientist box width = 300px name = James Joseph Sylvester image width = 300px caption = James Joseph Sylvester (1814 1897) birth date = birth date|1814|09|03 birth place = London, England death date = death date and… … Wikipedia
James Joseph Sylvester — James Joseph Sylvester, mathématicien et géomètre anglais, est né à Londres le 3 septembre 1814 et est décédé à Mayfair le 13 mars 1897. Il a commencé à enseigner les … Wikipédia en Français
Matrix determinant lemma — In mathematics, in particular linear algebra, the matrix determinant lemma[1][2] computes the determinant of the sum of an invertible matrix A and the dyadic product, u vT, of a column vector u and a row vector vT. Contents 1 Statemen … Wikipedia
List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… … Wikipedia
List of theorems — This is a list of theorems, by Wikipedia page. See also *list of fundamental theorems *list of lemmas *list of conjectures *list of inequalities *list of mathematical proofs *list of misnamed theorems *Existence theorem *Classification of finite… … Wikipedia
Matrix (mathematics) — Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column of a matrix A. In mathematics, a matrix (plural matrices, or less commonly matrixes)… … Wikipedia
algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… … Universalium
Valeur propre, vecteur propre et espace propre — Fig. 1. A étire le vecteur x sans changer sa direction. x est un vecteur propre pour A, pour la valeur propre λ. En mathématiques, et plus particulièrement en algèbre linéaire, le concept de vecteur propre est une notion algébrique s appliquant à … Wikipédia en Français
Arthur Cayley — Infobox Scientist name = Arthur Cayley |242px image width = 242px caption = Portrait in London by Barraud Jerrard birth date = birth date|1821|8|16|mf=y birth place = Richmond, Surrey, UK residence = England nationality = British death date =… … Wikipedia
