The identity matrix is a the simplest nontrivial diagonal matrix, defined such that
I(X) congruent X
for all vectors X. An identity matrix may be denoted 1, I, E (the latter being an abbreviation for the German term "Einheitsmatrix", p. 7), or occasionally I, with a subscript sometimes used to indicate the dimension of the matrix. Identity matrices are sometimes also known as unit matrices.
The n×n identity matrix is given explicitly by
I_(ij) = δ_(ij)
for i, j = 1, 2, ..., n, where δ_(ij) is the Kronecker delta.