Indefinite numerical range of $3\times 3$ matrices

N. Bebiano; J. da Providência; R. Teixeira

Displaying similar documents to “Indefinite numerical range of $3 \times 3$ matrices”

An envelope for the spectrum of a matrix

Panayiotis Psarrakos, Michael Tsatsomeros (2012)

Open Mathematics

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We introduce and study an envelope-type region ɛ(A) in the complex plane that contains the eigenvalues of a given n×n complex matrix A. ɛ(A) is the intersection of an infinite number of regions defined by cubic curves. The notion and method of construction of ɛ(A) extend the notion of the numerical range of A, F(A), which is known to be an intersection of an infinite number of half-planes; as a consequence, ɛ(A) is contained in F(A) and represents an improvement in localizing the spectrum...

The centre symmetry set

Peter Giblin, Paul Holtom (1999)

Banach Center Publications

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A centrally symmetric plane curve has a point called it’s centre of symmetry. We define (following Janeczko) a set which measures the central symmetry of an arbitrary strictly convex plane curve, or surface in $R^{3}$ . We investigate some of it’s properties, and begin the study of non-convex cases.