In probability theory, the matrix geometric method is a method for the analysis of quasi-birth–death processes, continuous-time Markov chain whose transition...

analysis in geometric optics, a mathematical method for performing ray tracing calculations. Transfer-matrix method (combinatorics), a method for computing...

in an M/G/1 queue. The method is a more complicated version of the matrix geometric method and is the classical solution method for M/G/1 chains. An M/G/1-type...

algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors...

{T}}} . The total geometric multiplicity γA is 2, which is the smallest it could be for a matrix with two distinct eigenvalues. Geometric multiplicities...

x_{k+1}=x_{k}+t=x_{k}-{\frac {f'(x_{k})}{f''(x_{k})}}.} The geometric interpretation of Newton's method is that at each iteration, it amounts to the fitting...

In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function...

character is encoded in the geometric-distance matrix. The geometric-distance matrix is a different type of distance matrix that is based on the graph-theoretical...

a square matrix are the roots of a polynomial determinant. In geometry, matrices are widely used for specifying and representing geometric transformations...

an invertible matrix is a square matrix that has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can...

iteratively from the Google matrix using the power method. However, in order for the power method to converge, the matrix must be stochastic, irreducible...

corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse...

in the ARPANET, a forerunner to the Internet. The matrix geometric method and matrix analytic methods have allowed queues with phase-type distributed inter-arrival...

In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative...

extremely diverse as they include Krylov subspace methods and can be preconditioned. Any geometric multigrid cycle iteration is performed on a hierarchy...

elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation...

In classical and quantum mechanics, geometric phase is a phase difference acquired over the course of a cycle, when a system is subjected to cyclic adiabatic...

multiplicities Geometric multiplicities of eigenvalues (but not the eigenspaces, which are transformed according to the base change matrix P used). Minimal...

for matrix-valued geometric series, function-valued geometric series, p {\displaystyle p} -adic number geometric series, and most generally geometric series...

for matrix-valued geometric series, function-valued geometric series, p {\displaystyle p} -adic number geometric series, and most generally geometric series...

rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [...

there exists an m × n {\displaystyle m\times n} matrix A {\displaystyle A} , called the transformation matrix of T {\displaystyle T} , such that: T ( x )...

question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a polytope. The shape of this polytope is defined by the...

vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial...

case for all rays must still focus the paraxial rays correctly, this matrix method will properly describe the positions of focal planes and magnifications...

linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an...

distribution of a quasi-birth-death process can be computed using the matrix geometric method. Latouche, G. (2011). "Level-Independent Quasi-Birth-and-Death...

{\displaystyle {\vec {v}}\!} , adding two matrices would have the geometric effect of applying each matrix transformation separately onto v → {\displaystyle {\vec...

{\displaystyle D^{2}f} is the 2nd derivative Hessian matrix). Newton's method is one of many known methods of computing square roots. Given a positive number...

{\displaystyle v} is normal to. In geometric optics, specular reflection can be expressed in terms of the Householder matrix (see Specular reflection § Vector...