Coefficient matrix

In linear algebra, the coefficient matrix refers to a matrix consisting of the coefficients of the variables in a set of linear equations.


In general, a system with m linear equations and n unknowns can be written as

a_{11}x_1 + a_{12}x_2 + ... + a_{1n}x_n = b_1 \,
a_{21}x_1 + a_{22}x_2 + ... + a_{2n}x_n = b_2 \,
\vdots \,
a_{m1}x_1 + a_{m2}x_2 + ... + a_{mn}x_n = b_m \,

where x_1,\ x_2,...,x_n are the unknowns and the numbers a_{11},\ a_{12},...,\ a_{mn} are the coefficients of the system. The coefficient matrix is the mxn matrix with the coefficient aij as the (i,j)-th entry:

a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix}

See also

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Matrix differential equation — A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and of its derivatives of various orders. A matrix differential equation is one containing more… …   Wikipedia

  • Matrix-free methods — In computational mathematics, a matrix free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly, but accesses the matrix by evaluating matrix vector… …   Wikipedia

  • Matrix mechanics — Quantum mechanics Uncertainty principle …   Wikipedia

  • Matrix coefficient — In mathematics, a matrix coefficient (or matrix element) is a function on a group of a special form, which depends on a linear representation of the group and additional data. For the case of a finite group, matrix coefficients express the action …   Wikipedia

  • Matrix multiplication — In mathematics, matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix. If A is an n by m matrix and B is an m by p matrix, the result AB of their multiplication is an n by p matrix defined only if… …   Wikipedia

  • Matrix exponential — In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.… …   Wikipedia

  • Coefficient — For other uses of this word, see coefficient (disambiguation). In mathematics, a coefficient is a multiplicative factor in some term of an expression (or of a series); it is usually a number, but in any case does not involve any variables of the… …   Wikipedia

  • Block matrix — In the mathematical discipline of matrix theory, a block matrix or a partitioned matrix is a matrix broken into sections called blocks. Looking at it another way, the matrix is written in terms of smaller matrices.[1] We group the rows and… …   Wikipedia

  • General matrix notation of a VAR(p) — This page just shows the details for different matrix notations of a VAR( p ) process with k variables. Var( p ):y {t}=c + A {1}y {t 1} + A {2}y {t 2} + cdots + A {p}y {t p} + e {t},Where each y {i} is a k x 1 vector and each A {i} is a k x k… …   Wikipedia

  • Multitrait-multimethod matrix — The multitrait multimethod (MTMM) matrix is an approach to examining Construct Validity developed by Campbell and Fiske(1959)[1]. There are six major considerations when examining a construct s validity through the MTMM matrix, which are as… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.