Joint zero sets and ranges of several Hermitian forms over complex and quaternionic scalars

P. Binding; A. Markus

doi:10.1016/S0024-3795(03)00493-2

Joint zero sets and ranges of several Hermitian forms over complex and quaternionic scalars

P. Binding, A. Markus

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let h_j:V→ ℝ, j=1,...,n, be Hermitian forms on a inner product space over double-struck F sign=ℂ or ℍ, and let h:V→ ℝⁿ have jth component h_j. We study path connectedness of the joint zero set h^-1(0)∩V₁ and convexity of the joint range h(V₁) for various values of n, where V₁ is the unit sphere of V.

Original language	English
Pages (from-to)	63-72
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	385
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(03)00493-2
State	Published - 1 Jul 2004

Keywords

Hausdorff-Toeplitz theorem
Hermitian form
Joint range
Joint zero set
Quaternionic inner product space

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/S0024-3795(03)00493-2

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title = "Joint zero sets and ranges of several Hermitian forms over complex and quaternionic scalars",

abstract = "Let hj:V→ ℝ, j=1,...,n, be Hermitian forms on a inner product space over double-struck F sign=ℂ or ℍ, and let h:V→ ℝn have jth component hj. We study path connectedness of the joint zero set h-1(0)∩V1 and convexity of the joint range h(V1) for various values of n, where V1 is the unit sphere of V.",

keywords = "Hausdorff-Toeplitz theorem, Hermitian form, Joint range, Joint zero set, Quaternionic inner product space",

author = "P. Binding and A. Markus",

note = "Funding Information: P. Binding{\textquoteright}s research was supported by NSERC of Canada. University of Calgary for support and hospitality.",

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doi = "10.1016/S0024-3795(03)00493-2",

language = "English",

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TY - JOUR

T1 - Joint zero sets and ranges of several Hermitian forms over complex and quaternionic scalars

AU - Binding, P.

AU - Markus, A.

N1 - Funding Information: P. Binding’s research was supported by NSERC of Canada. University of Calgary for support and hospitality.

PY - 2004/7/1

Y1 - 2004/7/1

N2 - Let hj:V→ ℝ, j=1,...,n, be Hermitian forms on a inner product space over double-struck F sign=ℂ or ℍ, and let h:V→ ℝn have jth component hj. We study path connectedness of the joint zero set h-1(0)∩V1 and convexity of the joint range h(V1) for various values of n, where V1 is the unit sphere of V.

AB - Let hj:V→ ℝ, j=1,...,n, be Hermitian forms on a inner product space over double-struck F sign=ℂ or ℍ, and let h:V→ ℝn have jth component hj. We study path connectedness of the joint zero set h-1(0)∩V1 and convexity of the joint range h(V1) for various values of n, where V1 is the unit sphere of V.

KW - Hausdorff-Toeplitz theorem

KW - Hermitian form

KW - Joint range

KW - Joint zero set

KW - Quaternionic inner product space

UR - http://www.scopus.com/inward/record.url?scp=2542490546&partnerID=8YFLogxK

U2 - 10.1016/S0024-3795(03)00493-2

DO - 10.1016/S0024-3795(03)00493-2

M3 - Article

AN - SCOPUS:2542490546

SN - 0024-3795

VL - 385

SP - 63

EP - 72

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

Joint zero sets and ranges of several Hermitian forms over complex and quaternionic scalars

Abstract

Keywords

ASJC Scopus subject areas

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