Geometrical and Spectral Properties of the Orthogonal Projections of the Identity. (9th May 2013)

• Record Type: Journal Article
• Authors: González, Luis; Suárez, Antonio; García, Dolores
• Other Names: Sivakumar K. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-05-09
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/435730
• Languages: English
• ISSNs: 1110-757X

Abstract

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.