Linear operators on matrices: the invariance of the decomposable numerical range. II

Tin-Yau Tam

doi:10.1016/0024-3795(87)90257-6

Linear operators on matrices: the invariance of the decomposable numerical range. II

Tin-Yau Tam

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

7 Citations (Scopus)

Abstract

Let n, m be positive integers, H a subgroup of the symmetric group of degree m, and χ:H→C a character of degree 1 on H. We defined the generalized mth decomposable numerical range of an n × n complex matrix A (associated with H and χ) to be the set W^*_m(A) = {(K(A)x^*,x^*){divides}x^*is decomposable, {norm of matrix}x^*{norm of matrix}=1}, where K(A) is the induced matrix of A associated with H and χ. We determine those linear operators on the vector space of n × n complex matrices which preserve the generalized mth decomposable numerical range of each n × n complex matrix. The result is a generalization of some works of Marcus, Filippenko, Pellegrini, and the author himself. © 1987.

Original language	English
Pages (from-to)	197-207
Journal	Linear Algebra and Its Applications
Volume	92
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(87)90257-6
Publication status	Published - Jul 1987
Externally published	Yes

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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title = "Linear operators on matrices: the invariance of the decomposable numerical range. II",

abstract = "Let n, m be positive integers, H a subgroup of the symmetric group of degree m, and χ:H→C a character of degree 1 on H. We defined the generalized mth decomposable numerical range of an n × n complex matrix A (associated with H and χ) to be the set W*m(A) = \{(K(A)x*,x*)\{divides\}x*is decomposable, \{norm of matrix\}x*\{norm of matrix\}=1\}, where K(A) is the induced matrix of A associated with H and χ. We determine those linear operators on the vector space of n × n complex matrices which preserve the generalized mth decomposable numerical range of each n × n complex matrix. The result is a generalization of some works of Marcus, Filippenko, Pellegrini, and the author himself. {\textcopyright} 1987.",

author = "Tin-Yau Tam",

note = "Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].",

year = "1987",

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journal = "Linear Algebra and Its Applications",

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TY - JOUR

T1 - Linear operators on matrices

T2 - the invariance of the decomposable numerical range. II

AU - Tam, Tin-Yau

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 1987/7

Y1 - 1987/7

N2 - Let n, m be positive integers, H a subgroup of the symmetric group of degree m, and χ:H→C a character of degree 1 on H. We defined the generalized mth decomposable numerical range of an n × n complex matrix A (associated with H and χ) to be the set W*m(A) = {(K(A)x*,x*){divides}x*is decomposable, {norm of matrix}x*{norm of matrix}=1}, where K(A) is the induced matrix of A associated with H and χ. We determine those linear operators on the vector space of n × n complex matrices which preserve the generalized mth decomposable numerical range of each n × n complex matrix. The result is a generalization of some works of Marcus, Filippenko, Pellegrini, and the author himself. © 1987.

AB - Let n, m be positive integers, H a subgroup of the symmetric group of degree m, and χ:H→C a character of degree 1 on H. We defined the generalized mth decomposable numerical range of an n × n complex matrix A (associated with H and χ) to be the set W*m(A) = {(K(A)x*,x*){divides}x*is decomposable, {norm of matrix}x*{norm of matrix}=1}, where K(A) is the induced matrix of A associated with H and χ. We determine those linear operators on the vector space of n × n complex matrices which preserve the generalized mth decomposable numerical range of each n × n complex matrix. The result is a generalization of some works of Marcus, Filippenko, Pellegrini, and the author himself. © 1987.

UR - https://www.scopus.com/pages/publications/0005212004

UR - https://www.scopus.com/pages/publications/0005212004#tab=impact

U2 - 10.1016/0024-3795(87)90257-6

DO - 10.1016/0024-3795(87)90257-6

M3 - RGC 21 - Publication in refereed journal

SN - 0024-3795

VL - 92

SP - 197

EP - 207

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

Linear operators on matrices: the invariance of the decomposable numerical range. II

Abstract

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