An Explicit Jordan Decomposition of Companion Matrices
نویسندگان
چکیده
منابع مشابه
An Explicit Jordan Decomposition of Companion Matrices
We derive a closed form for the Jordan decomposition of companion matrices including properties of generalized eigenvectors. As a consequence, we provide a formula for the inverse of confluent Vandermonde matrices and results on sensitivity of multiple roots of polynomials.
متن کاملExplicit polar decomposition of companion matrices
An explicit formula for the polar decomposition of an n n nonsingular companion matrix is derived. The proof involves the largest and smallest singular values of the companion matrix.
متن کاملSingular value decomposition of multi-companion matrices
We obtain the singular value decomposition of multi-companion matrices. We completely characterise the columns of the matrix U and give a simple formula for obtaining the columns of the other unitary matrix, V , from the columns of U . We also obtain necessary and sufficient conditions for the related matrix polynomial to be hyperbolic.
متن کاملThe polar decomposition of block companion matrices
Let L(λ) = Inλ m + Am−1λm−1 + · · ·+ A1λ + A0 be an n× n monic matrix polynomial, and let CL be the corresponding block companion matrix. In this note, we extend a known result on scalar polynomials to obtain a formula for the polar decomposition of CL when the matrices A0 and Pm−1 j=1 AjA ∗ j are nonsingular.
متن کاملExplicit polar decomposition of complex matrices
In [F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2 case, Linear Algebra Appl., 38:239–249, 1981], the author gives a representation for the factors of the polar decomposition of a nonsingular real square matrix of order 2. Uhlig’s formulae are generalized to encompass all nonzero complex matrices of order 2 as well as all order n complex matrices with ran...
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ژورنال
عنوان ژورنال: TEMA - Tendências em Matemática Aplicada e Computacional
سال: 2006
ISSN: 2179-8451,1677-1966
DOI: 10.5540/tema.2006.07.02.0209