Difference between revisions of "Identity matrix"
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:<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> matrix where the leading diagonal is ones and all other entries are zero. | + | The identity matrix is an <math>n\times n</math> matrix where the leading diagonal is ones and all other entries are zero. That is, <math>a_{ii} = 1</math>, and <math>a_{ij} = 0</math> whenever <math>i \neq j</math>. |
:<math>I=\begin{bmatrix} | :<math>I=\begin{bmatrix} | ||
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</math> | </math> | ||
| − | [[Category:Linear | + | [[Category:Linear Algebra]] |
Latest revision as of 14:34, July 28, 2016
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 matrix where the leading diagonal is ones and all other entries are zero. That is, 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 a_{ii} = 1} , and whenever .
- 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} }