On the maximal numerical range of some matrices

Ali N. Hamed, Ilya M. Spitkovsky

Research output: Contribution to journalArticlepeer-review


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
StatePublished - 2018


  • Maximal numerical range
  • Normaloid matrices
  • Numerical range

ASJC Scopus subject areas

  • Algebra and Number Theory


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