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Numerical Range of Matrix Polynomials
SIAM Journal on Matrix Analysis and Applications, 1994Let \(A_ i\), \(i = 1, \dots, m\) be \(n \times n\) matrices with complex coefficients and consider the matrix polynomial \(P(\lambda) = \sum_{i=0}^ m A_ i \lambda^ i\). The numerical range of \(P(\lambda)\) is defined through \[ W \bigl( P(\lambda) \bigr) : = \{\mu \in \mathbb{C} \mid x^* P(\mu)x = 0 \quad \text{for some nonzero} \quad x \in \mathbb{C}
Li, Chi-Kwong, Rodman, Leiba
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Essential numerical range and maximal numerical range of the Aluthge transform
Linear and Multilinear Algebra, 2007Let T be a bounded linear operator on a complex separable Hilbert space . Let and be the Aluthge transform and *-Aluthge transform of T respectively. In this article, we consider the essential numerical range and maximal numerical range of T, and . We prove that the essential numerical range of is always contained in that of T and is the same as that ...
Guoxing Ji, Ni Liu, Ze Li
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Generalized higher-rank numerical range
2012Summary: In this note, a generalization of higher rank numerical range is introduced and some of its properties are investigated.
AFSHIN, HAMID REZA +2 more
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The evolving landscape of salivary gland tumors
Ca-A Cancer Journal for Clinicians, 2023Conor Steuer
exaly
Top-down control of hippocampal signal-to-noise by prefrontal long-range inhibition
Cell, 2022Ruchi Malik, Vikaas S Sohal
exaly