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Linear and Multilinear Algebra Volume 11, 1982 - Issue 3
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Original Articles

Three elementary proofs of the goldberg-straus theorem on numerical radii

Marvin Marcus Institute for the Interdisciplinary Applications of Algebra and Combinatorics, University of California, Santa Barbara
&
Markus Sandy Institute for the Interdisciplinary Applications of Algebra and Combinatorics, University of California, Santa Barbara
Pages 243-252 | Received 01 Apr 1981, Published online: 30 May 2007

Citations (22)

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Read on this site (10)

Xingzhi Zhan. (2001) Span of the orthogonal orbit of real matrices. Linear and Multilinear Algebra 49:4, pages 337-346.
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Bit-Shun Tam. (1998) Exterior numerical radii and antiinvariant subspaces. Linear and Multilinear Algebra 44:3, pages 195-245.
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Tian-Gang Lei. (1998) Congruence numerical ranges and their radii. Linear and Multilinear Algebra 43:4, pages 411-427.
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Chi-Kwong Li. (1994) C-numerical ranges and C-numerical radii. Linear and Multilinear Algebra 37:1-3, pages 51-82.
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Tian-Gang Lei. (1993) On generalized numerical ranges with the induced matrix. Linear and Multilinear Algebra 34:3-4, pages 385-394.
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Chi-Kwong Li. (1991) Inequalities relating norms invariant under unitary similarities. Linear and Multilinear Algebra 29:3-4, pages 155-167.
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Chi-Kwong Li & Nam Kiu Tsing. (1989) Norms that are invariant under unitary similarities and the C-numerical radii. Linear and Multilinear Algebra 24:3, pages 209-222.
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Chi-Kwong Li & Nam-Kiu Tsing. (1988) Linear operators that preserve the c-numerical range or radius of matrices. Linear and Multilinear Algebra 23:1, pages 27-46.
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Tin-Yau Tam. (1986) On the generalized radial matrices and a conjecture of Marcus and Sandy. Linear and Multilinear Algebra 19:1, pages 11-20.
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Marvin Marcus & Markus Sandy. (1985) Singular values and numerical radii. Linear and Multilinear Algebra 18:4, pages 337-353.
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Articles from other publishers (12)

Pan-Shun Lau. (2018) Linear images of joint unitary orbits of Hermitian matrices. Linear Algebra and its Applications 542, pages 35-53.
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M. Günther & L. Klotz. (2014) Lieb functions and m-positivity of norms. Linear Algebra and its Applications 456, pages 54-63.
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Chi-Kwong Li & Nam-Kiu Tsing. (1995) Linear maps relating different unitary similarity orbits or different generalized numerical ranges. Linear Algebra and its Applications 223-224, pages 463-481.
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Chi-Kwong Li. (1994) Some aspects of the theory of norms. Linear Algebra and its Applications 212-213, pages 71-100.
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Robert Grone. (1994) A biography of Marvin Marcus. Linear Algebra and its Applications 201, pages 1-20.
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Chi-Kwong Li & Nam-Kiu Tsing. (1991) G-invariant norms and G(c)-radii. Linear Algebra and its Applications 150, pages 179-194.
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Roger A. Horn & Roy Mathias. (1990) An Analog of the Cauchy–Schwarz Inequality for Hadamard Products and Unitarily Invariant Norms. SIAM Journal on Matrix Analysis and Applications 11:4, pages 481-498.
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Bit-Shun Tam. (2009) A Simple proof of the Goldberg–Straus theorem on numerical radii. Glasgow Mathematical Journal 28:2, pages 139-141.
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Marvin Marcus & Markus Sandy. (1985) Conditions for the generalized numerical range to be real. Linear Algebra and its Applications 71, pages 219-239.
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Moshe Goldberg & E.G. Straus. (1983) Multiplicativity factors for C-numerical radii. Linear Algebra and its Applications 54, pages 1-16.
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Moshe Goldberg & E. G. Straus. 1983. General Inequalities 3. General Inequalities 3 195 204 .
Moshe Goldberg & E.G. Straus. (1982) Operator norms, multiplicativity factors, and C-numerical radii. Linear Algebra and its Applications 43, pages 137-159.
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