Identity matrix: Difference between revisions
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imported>Richard Pinch (ref to identity map) |
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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]]. | 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 map|identity]] [[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]]. | ||
Revision as of 12:33, 13 December 2008
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 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.