### Abstract

The maximal numerical range W_{0}(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 W_{0}(A) ⊆ W (A). Conditions under which W_{0}(A) has a non-empty intersection with the boundary of W (A) are established, in particular, when W_{0}(A) = W (A). The set W_{0}(A) is also described explicitly for matrices unitarily similar to direct sums of 2-by-2 blocks, and some insight into the behavior of W_{0}(A) is provided when L has codimension one.

Original language | English (US) |
---|---|

Article number | 21 |

Pages (from-to) | 288-303 |

Number of pages | 16 |

Journal | Electronic Journal of Linear Algebra |

Volume | 34 |

DOIs | |

State | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Maximal numerical range
- Normaloid matrices
- Numerical range

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Electronic Journal of Linear Algebra*,

*34*, 288-303. [21]. https://doi.org/10.13001/1081-3810,1537-9582.3774

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

Research output: Contribution to journal › Article

*Electronic Journal of Linear Algebra*, vol. 34, 21, pp. 288-303. https://doi.org/10.13001/1081-3810,1537-9582.3774

}

TY - JOUR

T1 - On the maximal numerical range of some matrices

AU - Hamed, Ali N.

AU - Spitkovsky, Ilya

PY - 2018/1/1

Y1 - 2018/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=85055735860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055735860&partnerID=8YFLogxK

U2 - 10.13001/1081-3810,1537-9582.3774

DO - 10.13001/1081-3810,1537-9582.3774

M3 - Article

AN - SCOPUS:85055735860

VL - 34

SP - 288

EP - 303

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

SN - 1081-3810

M1 - 21

ER -