Definitions for identity matrix
This page provides all possible meanings and translations of the word identity matrix
identity matrix, unit matrix(noun)
a scalar matrix in which all of the diagonal elements are unity
A diagonal matrix all of the diagonal elements of which are equal to 1.
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.
Translations for identity matrix
From our Multilingual Translation Dictionary
- matriz identidadSpanish
- identiteettimatriisi, yksikkömatriisiFinnish
- matrice identité, matrice unitéFrench
- egységmátrix, identitásmátrixHungarian
- matrice identitàItalian
- macierz jednostkowaPolish
- едини́чная ма́трицаRussian
Get even more translations for identity matrix »
Find a translation for the identity matrix definition in other languages:
Select another language:
Discuss these identity matrix definitions with the community:
Word of the Day
Would you like us to send you a FREE new word definition delivered to your inbox daily?
Use the citation below to add this definition to your bibliography:
"identity matrix." Definitions.net. STANDS4 LLC, 2015. Web. 31 Mar. 2015. <http://www.definitions.net/definition/identity matrix>.