Geometrical and Spectral Properties of the Orthogonal Projections of the Identity. (9th May 2013) - González, Luis; Suárez, Antonio; García, Dolores
Abstract : We analyze the best approximation A N (in the Frobenius sense) to the identity matrix in an arbitrary matrix subspace A S (A ∈ ℝ n × n nonsingular, S being any fixed subspace of ℝ n × n ). Some new geometrical and spectral properties of the orthogonal projection A N are derived. In particular, new inequalities for the trace and for the eigenvalues of matrix A N are presented for the special case that A N is symmetric and positive definite.