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| Titel: |
Bounds for the spectral norm of certain matrices |
| Auteur: |
London, David Schwarz, Binyamin Zaks, Abraham |
| Verschenen in: |
Linear & multilinear algebra |
| Paginering: | Jaargang 19 (1986) nr. 1 pagina's 57-66 |
| Jaar: |
1986-04 |
| Inhoud: |
Let αi and βji = 1, … n, be nonnegative numbers such that α + β ≤ π/2, where α = max{αi}, and β = max{βi}. Let U = (uij) and V = (vij) be n × n unitary matrices, let W = (wij), where wij = uijsin αi cos β j+vijcos α;i sib βj, i,j = 1, …, n, and let ‖ ‖ denote the spectral norm. In a previous paper it was proved that [image omitted] Here we prove that [image omitted] Each inequality implies, and is equivalent to, the triangle inequality for the recently constructed spherical distance of a projective matrix space, and the validity of either of these inequalities is needed to construct this distance function. Hence, the two inequalities are equivalent. These geometric considerations allow us thus to obtain inequality (i) from the easily proved (ii). Our direct proofs of (i) and (ii) establish their validity for wider classes of matrices and we start the paper with a brief discussion of these classes. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 2 van 8 gevonden artikelen
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