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Keywords
(6)
Bilinear Form
Canonical Form
Indefinite Inner Product
Normal Matrices
Normal Matrix
Spectrum
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ESSENTIAL DECOMPOSITION OF POLYNOMIALLY NORMAL MATRICES IN REAL INDEFINITE INNER PRODUCT SPACES
ESSENTIAL DECOMPOSITION OF POLYNOMIALLY NORMAL MATRICES IN REAL INDEFINITE INNER PRODUCT SPACES,CHRISTIAN MEHL
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ESSENTIAL DECOMPOSITION OF POLYNOMIALLY NORMAL MATRICES IN REAL INDEFINITE INNER PRODUCT SPACES
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Citations: 2
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CHRISTIAN MEHL
Polynomially
normal matrices
in real
indefinite inner product
spaces are studied, i.e., matrices whose adjoint with respect to the
indefinite inner product
is a polynomial in the matrix. The set of these matrices is a subset of
indefinite inner product
normal matrices
that contains all selfadjoint, skewadjoint, and unitary matrices, but that is small enough such that all elements can be completely classified. The essential decomposition of a real polynomially
normal matrix
is introduced. This is a decomposition into three parts, one part having real
spectrum
only and two parts that can be described by two complex matrices that are polynomially normal with respect to a sesquilinear and bilinear form, respectively. In the paper, the essential decomposition is used as a tool in order to derive a sucient condition for existence of invariant semidefinite subspaces and to obtain canonical forms for real polynomially normal matrices. In particular, canonical forms for real matrices that are selfadjoint, skewadjoint, or unitary with respect to an
indefinite inner product
are recovered.
Published in 2006.
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Citation Context
(1)
...However, the investigation of the real case in full detail needs additional discussions and is referred to the subsequent paper [
18
]...
...For the case of a nonreal spectrum, further considerations are necessary, see [
18
] for details...
CHRISTIAN MEHL
.
ON CLASSIFICATION OF NORMAL MATRICES IN INDEFINITE INNER PRODUCT SPACE...
References
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WenWei Lin
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, vol. 302, no. 13, pp. 469533, 1999
ON CLASSIFICATION OF NORMAL MATRICES IN INDEFINITE INNER PRODUCT SPACES
(
Citations: 8
)
CHRISTIAN MEHL
Published in 2006.
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Citations
(2)
Supernormal mappings: Part 1. Orthogonally indecomposable modules and applications
Olaf v. Grudzinski
,
Frieder Knüppel
,
Klaus Nielsen
Journal:
Linear Algebra and Its Applications  LINEAR ALGEBRA APPL
, vol. 431, no. 1, pp. 3955, 2009
ON CLASSIFICATION OF NORMAL MATRICES IN INDEFINITE INNER PRODUCT SPACES
(
Citations: 8
)
CHRISTIAN MEHL
Published in 2006.