TY - JOUR

T1 - On the maximal numerical range of some matrices

AU - Hamed, Ali N.

AU - Spitkovsky, Ilya M.

N1 - Funding Information:
‡Division of Science and Mathematics, New York University Abu Dhabi (NYUAD), Saadiyat Island, P.O. Box 129188, Abu Dhabi, United Arab Emirates ([email protected], [email protected]). Supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi.
Publisher Copyright:
© 2018, International Linear Algebra Society. All rights reserved.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Maximal numerical range

KW - Normaloid matrices

KW - Numerical range

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U2 - 10.13001/1081-3810.3774

DO - 10.13001/1081-3810.3774

M3 - Article

AN - SCOPUS:85055735860

SN - 1537-9582

VL - 34

SP - 288

EP - 303

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

M1 - 21

ER -