identity matrix

The n×n identity matrixMathworldPlanetmath I (or In) over a ring R (with an identityPlanetmathPlanetmathPlanetmath 1) is the square matrixMathworldPlanetmath with coefficients in R given by


where the numeral “1” and “0” respectively represent the multiplicative and additive identities in R.

0.0.1 Properties

The identity matrix In serves as the multiplicative identityPlanetmathPlanetmath in the ring of n×n matrices over R with standard matrix multiplication. For any n×n matrix M, we have InM=MIn=M, and the identity matrix is uniquely defined by this property. In additionPlanetmathPlanetmath, for any n×m matrix A and m×n B, we have IA=A and BI=B.

The n×n identity matrix I satisfy the following properties

Title identity matrix
Canonical name IdentityMatrix
Date of creation 2013-03-22 12:06:29
Last modified on 2013-03-22 12:06:29
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 13
Author mathcam (2727)
Entry type Definition
Classification msc 15-01
Classification msc 15A57
Related topic KroneckerDelta
Related topic ZeroMatrix
Related topic IdentityMap