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_(i j) = δ_(i j) for i, j = 1, 2, ..., n, where δ_(i j) is the Kronecker delta.
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