Index: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Home > Matrix decomposition

In the mathematical discipline of linear algebra, a matrix decomposition is a factorization of a matrix into some canonical form. There are several different decompositions of a given matrix and the decomposition used depends on the problem we want to solve. In numerical analysis for example different decompositions are used to implement efficient matrix algorithms.

1 Example

When solving a system of linear equations the matrix A can be decomposed via the LU decomposition. The LU decomposition factorizes a matrix into a lower triangular matrix L and an upper triangular matrix U. The matrices L and U are much easier to solve than the original matrix A.

2 See also

Topics in mathematics related to linear algebra	Edit
Vectors \| Vector spaces \| Linear span \| Linear transformation \| Linear independence \| Linear combination \| Basis \| Column space \| Row space \| Dual space \| Orthogonality \| Eigenvector \| Eigenvalue \| Least squares regressions \| Outer product \| Cross product \| Dot product \| Transpose \| Matrix decomposition

Abstract algebraAbstract algebra Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. The term "abstract algebra" is used to distinguish the field from " elementary algebra" or "high school algebr AlgebraAlgebra Algebra (from the Arabic al-jabr meaning reunion connection or completion is a branch of mathematics which may be roughly characterized as a generalization and extension of arithmetic; it also refers to a particular kind of abstract algebra struct Linear algebra Matrix theoryIn mathematics, matrix theory is a branch of mathematics which focuses on the study of matrices. Initially, a sub-branch of linear algebra, it soon grew to cover subjects related to graph theory, algebra, combinatorics and statistics as well. History The

Read more »

<Hide>

Topics: Matrix Decomposition, Matrix (mathematics), Matrix Addition...

MatrixMatrix (plural matrices has several meanings. Generally speaking, a matrix is something that provides support or structure, especially in the sense of surrounding and/or shaping. It comes from the Latin word for "womb", which itself derived from the Latin	Matrix (mathematics)Abstract algebra Algebra Linear algebra In mathematics, a matrix (plural matrices is a rectangular table of numbers or, more generally, of elements of a fixed ring. In this article, if unspecified, the entries of a matrix are always real or complex number	Matrix additionThe usual matrix addition is defined for two matrices of same dimensions. The sum of two m by n matrices A and B denoted by A + B is again an m by n matrix computed by adding corresponding elements, i. A + B i, j A ''i, j + B ''i, j . For example : The m
Matrix multiplicationThis article gives an overview of the various ways to multiply matrices. The Einstein notation is used throughout. Ordinary matrix product By far the most important way to multiply matrices is the usual matrix multiplication. It is defined between two mat	Matrix inversionMatrix inversion is the following problem in linear algebra: given a square n by n matrix A find a square n by n matrix B (if one exists) such that AB BA I the n by n identity matrix. The Gauss-Jordan elimination is an algorithm that can be used to determ	Matrix representation of conic sectionsIn mathematics, the matrix representation of conic sections is one way of studying a conic section, its axis, vertices, foci, tangents, and the relative position of a given point. We can also study conic sections whose axes aren't parallel to our coordina
Matrix norm	Matrix theory	Matrix decomposition
Matrix series	Matrix mechanics	Matrix wipe
Matrix theory (physics)	Matrix normal distribution	Matrix ring

Non User