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- Identity_matrix abstract "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. (In some fields, such as quantum mechanics, the identity matrix is denoted by a boldface one, 1; otherwise it is identical to I.) Some mathematics books use U and E to represent the Identity Matrix (meaning "Unit Matrix" and the German word "Einheitsmatrix", respectively), although I is considered more universal.[citation needed]When A is m×n, it is a property of matrix multiplication thatIn 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(n) consisting of all invertible n×n matrices. (The identity matrix itself is invertible, being its own inverse.)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.Using the notation that is sometimes used to concisely describe diagonal matrices, we can write:It can also be written using the Kronecker delta notation:The identity matrix also has the property that, when it is the product of two square matrices, the matrices can be said to be the inverse of one another.The identity matrix of a given size is the only idempotent matrix of that size having full rank. That is, it is the only matrix such that (a) when multiplied by itself the result is itself, and (b) all of its rows, and all of its columns, are linearly independent.The principal square root of an identity matrix is itself, and this is its only positive definite square root. However, every identity matrix with at least two rows and columns has an infinitude of symmetric square roots.".
- Identity_matrix wikiPageID "59718".
- Identity_matrix wikiPageRevisionID "580335225".
- Identity_matrix hasPhotoCollection Identity_matrix.
- Identity_matrix id "1223".
- Identity_matrix title "Identity matrix".
- Identity_matrix subject Category:Abstract_algebra.
- Identity_matrix subject Category:Linear_algebra.
- Identity_matrix subject Category:Matrices.
- Identity_matrix subject Category:One.
- Identity_matrix subject Category:Sparse_matrices.
- Identity_matrix comment "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.".
- Identity_matrix label "Eenheidsmatrix".
- Identity_matrix label "Einheitsmatrix".
- Identity_matrix label "Identity matrix".
- Identity_matrix label "Macierz jednostkowa".
- Identity_matrix label "Matrice identità".
- Identity_matrix label "Matrice identité".
- Identity_matrix label "Matriz identidad".
- Identity_matrix label "Matriz identidade".
- Identity_matrix label "Единичная матрица".
- Identity_matrix label "مصفوفة الوحدة".
- Identity_matrix label "単位行列".
- Identity_matrix label "單位矩陣".
- Identity_matrix sameAs Jednotková_matice.
- Identity_matrix sameAs Einheitsmatrix.
- Identity_matrix sameAs Matriz_identidad.
- Identity_matrix sameAs Unitate_matrize.
- Identity_matrix sameAs Matrice_identité.
- Identity_matrix sameAs Matrice_identità.
- Identity_matrix sameAs 単位行列.
- Identity_matrix sameAs 단위행렬.
- Identity_matrix sameAs Eenheidsmatrix.
- Identity_matrix sameAs Macierz_jednostkowa.
- Identity_matrix sameAs Matriz_identidade.
- Identity_matrix sameAs m.0g816.
- Identity_matrix sameAs Q193794.
- Identity_matrix sameAs Q193794.
- Identity_matrix wasDerivedFrom Identity_matrix?oldid=580335225.
- Identity_matrix isPrimaryTopicOf Identity_matrix.