# Definitions for **identity matrix**

### This page provides all possible meanings and translations of the word **identity matrix**

### Princeton's WordNet

identity matrix, unit matrix(noun)

a scalar matrix in which all of the diagonal elements are unity

### Wiktionary

identity matrix(Noun)

A diagonal matrix all of the diagonal elements of which are equal to 1.

### Freebase

Identity matrix

In linear algebra, the identity matrix or unit matrix of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context. Some mathematics books use U and E to represent the Identity Matrix, although I is considered more universal. When A is m×n, it is a property of matrix multiplication that In particular, the identity matrix serves as the unit of the ring of all n×n matrices, and as the identity element of the general linear group GL consisting of all invertible n×n matrices. Where n×n matrices are used to represent linear transformations from an n-dimensional vector space to itself, In represents the identity function, regardless of the basis. The ith column of an identity matrix is the unit vector ei. It follows that the determinant of the identity matrix is 1 and the trace is n.

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"identity matrix." *Definitions.net.* STANDS4 LLC, 2014. Web. 17 Dec. 2014. <http://www.definitions.net/definition/identity matrix>.