Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online lexicon:

Linear Systems of Equations

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 overview
A linear system of equations (LSE) over a field $ K$ is given by

$\displaystyle \begin{array}{ccccccc} a_{1,1}x_1 & + & \cdots & + & a_{1,n}x_n ... ... & + & a_{m,n}x_n & = & b_m \end{array} \quad \leftrightarrow \quad Ax = b $

with coefficient matrix $ A = (a_{i,j})\in K^{m\times n}$, 'unknown' $ x\in K^n$ and right hand side $ b\in K^m$.

The LSE is called homogeneous if $ b = 0$. Otherwise it is called inhomogeneous.

[Examples] [Links]
  automatically generated 5/23/2011