Geometrical and Spectral Properties of the Orthogonal Projections of the Identity

[摘要] We analyze the best approximationAN(in the Frobenius sense) to the identity matrix in an arbitrary matrix subspaceAS(A∈ℝn×nnonsingular,Sbeing any fixed subspace ofℝn×n). Some new geometrical and spectral properties of the orthogonal projectionANare derived. In particular, new inequalities for the trace and for the eigenvalues of matrixANare presented for the special case thatANis symmetric and positive definite.

[学科分类] 应用数学