Identity matrix: Difference between revisions
Jump to navigation
Jump to search
imported>Richard Pinch (ref to identity map) |
imported>Paul Wormer No edit summary |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
{{subpages}} | {{subpages}} | ||
In [[matrix algebra]], the '''identity matrix''' is a [[square matrix]] which has all the entries on the main [[diagonal]] equal to one and all the other, off-diagonal, entries equal to zero. The identity matrix acts as the [[identity element]] for [[matrix multiplication]]. Its entries are those of the [[Kronecker delta]]. The identity matrix represents the [[identity | In [[matrix algebra]], the '''identity matrix''' is a [[square matrix]] which has all the entries on the main [[diagonal]] equal to one and all the other, off-diagonal, entries equal to zero. The identity matrix acts as the [[identity element]] for [[matrix multiplication]]. Its entries are those of the [[Kronecker delta]]. The identity matrix represents the [[identity function]] as a [[linear map|linear operator]] on a [[vector space]]. | ||
The identity matrix is also known as '''unit matrix''' because it possesses many of the properties of the multiplicative unit of an algebraic [[field theory (mathematics)|field]]. | The identity matrix is also known as '''unit matrix''' because it possesses many of the properties of the multiplicative unit of an algebraic [[field theory (mathematics)|field]]. | ||
:<math> | |||
\mathbf{E}\; \stackrel{\mathrm{def}}{=}\; | |||
\begin{pmatrix} | |||
1 & 0 & 0 & \cdots & 0 \\ | |||
0 & 1 & 0 & \cdots & 0 \\ | |||
0 & 0 & 1 & \cdots & 0 \\ | |||
\vdots&& \ddots& &\vdots \\ | |||
\cdots &\cdots& &\\ | |||
0 & 0 & \cdots& 0 & 1 \\ | |||
\end{pmatrix} | |||
</math> | |||
The identity matrix is often indicated by '''E''' from the German ''Einheitsmatrix'' (unit matrix); '''I''' (from identity) is used as well. | |||
Latest revision as of 10:39, 23 April 2009
In matrix algebra, the identity matrix is a square matrix which has all the entries on the main diagonal equal to one and all the other, off-diagonal, entries equal to zero. The identity matrix acts as the identity element for matrix multiplication. Its entries are those of the Kronecker delta. The identity matrix represents the identity function as a linear operator on a vector space.
The identity matrix is also known as unit matrix because it possesses many of the properties of the multiplicative unit of an algebraic field.
The identity matrix is often indicated by E from the German Einheitsmatrix (unit matrix); I (from identity) is used as well.