On the maximal numerical range of some matrices

Ali N. Hamed, Ilya Spitkovsky

Research output: Contribution to journalArticle

Abstract

The maximal numerical range W0(A) of a matrix A is the (regular) numerical range W (B) of its compression B onto the eigenspace L of A*A corresponding to its maximal eigenvalue. So, always W0(A) ⊆ W (A). Conditions under which W0(A) has a non-empty intersection with the boundary of W (A) are established, in particular, when W0(A) = W (A). The set W0(A) is also described explicitly for matrices unitarily similar to direct sums of 2-by-2 blocks, and some insight into the behavior of W0(A) is provided when L has codimension one.

Original languageEnglish (US)
Article number21
Pages (from-to)288-303
Number of pages16
JournalElectronic Journal of Linear Algebra
Volume34
DOIs
StatePublished - Jan 1 2018

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Numerical Range
Eigenspace
Direct Sum
Codimension
Compression
Intersection
Eigenvalue

Keywords

  • Maximal numerical range
  • Normaloid matrices
  • Numerical range

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On the maximal numerical range of some matrices. / Hamed, Ali N.; Spitkovsky, Ilya.

In: Electronic Journal of Linear Algebra, Vol. 34, 21, 01.01.2018, p. 288-303.

Research output: Contribution to journalArticle

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