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

    Fingerprint

    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

    Hamed, Ali N. ; Spitkovsky, Ilya. / On the maximal numerical range of some matrices. In: Electronic Journal of Linear Algebra. 2018 ; Vol. 34. pp. 288-303.
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