Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2012), Article ID 435730, 8 pages.

Geometrical and Spectral Properties of the Orthogonal Projections of the Identity

Luis González, Antonio Suárez, and Dolores García

Full-text: Open access

Abstract

We analyze the best approximation A N (in the Frobenius sense) to the identity matrix in an arbitrary matrix subspace A S ( A n × n nonsingular, S being any fixed subspace of 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.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2012), Article ID 435730, 8 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807323

Digital Object Identifier
doi:10.1155/2013/435730

Mathematical Reviews number (MathSciNet)
MR3056204

Zentralblatt MATH identifier
1268.15019

Citation

González, Luis; Suárez, Antonio; García, Dolores. Geometrical and Spectral Properties of the Orthogonal Projections of the Identity. J. Appl. Math. 2013, Special Issue (2012), Article ID 435730, 8 pages. doi:10.1155/2013/435730. https://projecteuclid.org/euclid.jam/1394807323


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