Difference between revisions of "Identity matrix"
m (cat) |
(Added nouns to sentences, fixed grammar and spelling.) |
||
| Line 1: | Line 1: | ||
| − | In mathematics the '''identity matrix''' is the which does not change the size or values of | + | In mathematics the '''identity matrix''' is the [[matrix]] which, when [[multiplication|multiplying]], does not change the size or values of the matrix by which it is multiplied. The identity matrix is usually denoted <math>I</math> or <math>I_n</math>, and the operation of multiplication is described as, |
:<math>AI=A</math> or <math>IA=A</math> | :<math>AI=A</math> or <math>IA=A</math> | ||
| − | The identity matrix is an <math>n\times n</math> | + | The identity matrix is an <math>n\times n</math> matrix where the leading diagonal is ones and all other entries are zero. |
:<math>I=\begin{bmatrix} | :<math>I=\begin{bmatrix} | ||
| Line 10: | Line 10: | ||
\vdots & \vdots & \ddots & \vdots \\ | \vdots & \vdots & \ddots & \vdots \\ | ||
0 & 0 & \cdots & 1 \end{bmatrix} | 0 & 0 & \cdots & 1 \end{bmatrix} | ||
| − | </math> | + | </math> |
[[Category:Linear algebra]] | [[Category:Linear algebra]] | ||
Revision as of 16:30, April 21, 2011
In mathematics the identity matrix is the matrix which, when multiplying, does not change the size or values of the matrix by which it is multiplied. The identity matrix is usually denoted Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I_n} , and the operation of multiplication is described as,
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle AI=A} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle IA=A}
The identity matrix is an Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n\times n} matrix where the leading diagonal is ones and all other entries are zero.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I=\begin{bmatrix} 1 & 0 & \cdots & 0 \\ 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & 1 \end{bmatrix} }