invert a matrix
1Invertible matrix — In linear algebra an n by n (square) matrix A is called invertible (some authors use nonsingular or nondegenerate) if there exists an n by n matrix B such that where In denotes the n by n identity matrix and the multiplication used is ordinary… …
2Rotation matrix — In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix rotates points in the xy Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian… …
3Linear model — In statistics the linear model is given by:Y = X eta + varepsilonwhere Y is an n times;1 column vector of random variables, X is an n times; p matrix of known (i.e. observable and non random) quantities, whose rows correspond to statistical… …
4Inverse problem — An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in. For example, if we have measurements of the Earth s gravity field, then we might …
5Comparison of vector algebra and geometric algebra — Vector algebra and geometric algebra are alternative approaches to providing additional algebraic structures on vector spaces, with geometric interpretations, particularly vector fields in multivariable calculus and applications in mathematical… …
6Geometric algebra — In mathematical physics, a geometric algebra is a multilinear algebra described technically as a Clifford algebra over a real vector space equipped with a non degenerate quadratic form. Informally, a geometric algebra is a Clifford algebra that… …
7cryptology — cryptologist, n. cryptologic /krip tl oj ik/, cryptological, adj. /krip tol euh jee/, n. 1. cryptography. 2. the science and study of cryptanalysis and cryptography. [1635 45; < NL cryptologia. See CRYPTO , LOGY] * * * Introduction …
8Binomial inverse theorem — In mathematics, the binomial inverse theorem is useful for expressing matrix inverses in different ways.If A, U, B, V are matrices of sizes p × p , p × q , q × q , q × p , respectively, then:left(mathbf{A}+mathbf{UBV} ight)^{ 1}=mathbf{A}^{ 1}… …
9Legendre transformation — f(x) . The function is shown in red, and the tangent line at point (x 0, f(x 0)) is shown in blue. The tangent line intersects the vertical axis at (0, f^star) and f^star is the value of the Legendre transform f^star(p 0) , where p 0=dot{f}(x 0) …
10Canonical transformation — In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (mathbf{q}, mathbf{p}, t) ightarrow (mathbf{Q}, mathbf{P}, t) that preserves the form of Hamilton s equations, although it might not preserve the… …
