An envelope for the spectrum of a matrix

Panayiotis Psarrakos; Michael Tsatsomeros

Displaying similar documents to “An envelope for the spectrum of a matrix”

Indefinite numerical range of $3 \times 3$ matrices

N. Bebiano, J. da Providência, R. Teixeira (2009)

Czechoslovak Mathematical Journal

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The point equation of the associated curve of the indefinite numerical range is derived, following Fiedler’s approach for definite inner product spaces. The classification of the associated curve is presented in the $3 \times 3$ indefinite case, using Newton’s classification of cubic curves. Illustrative examples of all the different possibilities are given. The results obtained extend to Krein spaces results of Kippenhahn on the classical numerical range.

The higher rank numerical range of nonnegative matrices

Aikaterini Aretaki, Ioannis Maroulas (2013)

Open Mathematics

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In this article the rank-k numerical range ∧k (A) of an entrywise nonnegative matrix A is investigated. Extending the notion of elements of maximum modulus in ∧k (A), we examine their location on the complex plane. Further, an application of this theory to ∧k (L(λ)) of a Perron polynomial L(λ) is elaborated via its companion matrix C L.