Field Convexity of a Square Matrix

Moyls, B. N.; Marcus, M. D.

doi:10.2307/2033121

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) W M (A)dp M (A)1

Preliminary Materials1

Proof1

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1972

2018

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Cited by 5 publications

(5 citation statements)

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“…Our main purpose is to discuss the question of a converse: does m-convexity for certain values of m imply normality? Initial results in this direction were previously obtained by two of the authors [6], who proved that convexity guarantees normality when n S 4 but not when n ^ 5. An immediate corollary of this theorem is that if A (E M n (C) is normal, then A is m-convex for 1 S rn ^ n.…”

Section: ) W M (A)dp M (A)mentioning

confidence: 98%

Normality and the Higher Numerical Range

1978

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Let Mn(C) be the vector space of all w-square complex matrices. Denote by (• , •) the standard inner product in the space C n of complex n-tuples. For a matrix A ∈ Mn(C) and an n-tuple c = (c1,… , cn) ∈ C n, define the c-numerical range of A to be the set

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Section: ) W M (A)dp M (A)mentioning

confidence: 98%

Normality and the Higher Numerical Range

1978

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“…In this case, C must be normal [9]. From (34) we compute that CC* = diag(1, ei'") 2d 1 diag(l, e-").…”

Section: Preliminary Materialsmentioning

confidence: 99%

“…By[9] again, C is not normal. We show that Both 1 and eiw are main diagonal elements of C and hence are in W(C).…”

mentioning

confidence: 94%

Singular values and numerical radii

Marcus

Sandy

1985

Linear and Multilinear Algebra

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“…In [6] Moyls and Marcus obtain conditions which are necessary and sufficient for an operator on a finite dimensional Hilbert space to be convexoid. The next result is somewhat simpler than their theorem.…”

Section: Proofmentioning

confidence: 99%