Any square matrix with elements ij such that ij = 1 if = and ij = 0 otherwise. A point or vector that is transformed by the identity matrix remains unchanged.
a scalar matrix in which all of the diagonal elements are unity
a square matrix, called I , that has ones down the leading diagonal (see the examples below) and zeros everywhere else
a square matrix of any dimension whose elements are ones on its northwest-to-southeast diagonal and zeroes everywhere else
a square matrix with ones along the diagonal and zeros elsewhere
a trivial permutation matrix
Matrix embodying the null transformation that maps any vector to itself.
A scoring matrix in which only identical characters receive a positive score; the matrix has ones along the main diagonal and zeroes elsewhere.
In linear algebra, the identity matrix of size n is the n-by-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.)