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A conjectured property of Hermitian pencils

โœ Scribed by William C. Waterhouse

Book ID
107824966
Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
280 KB
Volume
51
Category
Article
ISSN
0024-3795

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Let M n be the algebra of all n ร— n complex matrices. For 1 ~< k ~< n, the kth numerical range of A 6 M, is defined by Wk(A) = {(i/k)E~=,x\*~Axj: {x t ..... x k} is an orthonormal set in C"}. It is known that {tr A/n} = W,(A) ~ W n\_ 1(A) c\_ ... c\_ WI(A). We study the condition on A under which W~