Geometrical and Spectral Properties of the Orthogonal Projections of the Identity
We analyze the best approximation (in the Frobenius sense) to the identity matrix in an arbitrary matrix subspace ( nonsingular, being any fixed subspace of ). Some new geometrical and spectral properties of the orthogonal projection are derived. In particular, new inequalities for the trace and...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/435730 |
| Summary: | We analyze the best approximation (in the Frobenius sense) to the identity matrix in an arbitrary matrix subspace ( nonsingular, being any fixed subspace of ). Some new geometrical and spectral properties of the orthogonal projection are derived. In particular, new inequalities for the trace and for the eigenvalues of matrix are presented for the special case that is symmetric and positive definite. |
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| ISSN: | 1110-757X 1687-0042 |