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2015 Higher rank numerical ranges of rectangular matrices
Gholamreza Aghamollaei, Mohsen Zahraei
Ann. Funct. Anal. 6(2): 133-142 (2015). DOI: 10.15352/afa/06-2-12


In this paper, the notions of rank$-k$ numerical range and $k-$spectrum of rectangular complex matrices are introduced. Some algebraic and geometrical properties are investigated. Moreover, for $\epsilon \gt 0,$ the notion of Birkhoff-James approximate orthogonality sets for $\epsilon$-higher rank numerical ranges of rectangular matrices is also introduced and studied. The proposed definitions yield a natural generalization of standard higher rank numerical ranges.


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Gholamreza Aghamollaei. Mohsen Zahraei. "Higher rank numerical ranges of rectangular matrices." Ann. Funct. Anal. 6 (2) 133 - 142, 2015.


Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 06441294
MathSciNet: MR3292521
Digital Object Identifier: 10.15352/afa/06-2-12

Primary: 15A60
Secondary: 15A18‎ , 47A30 , 81P68

Keywords: $k-$spectrum , isometry , numerical range , Rank$-k$ numerical range , rectangular matrices

Rights: Copyright © 2015 Tusi Mathematical Research Group

Vol.6 • No. 2 • 2015
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