Partial orderings, preorderings, and the polar decomposition of matrices
نویسندگان
چکیده
منابع مشابه
The 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 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.
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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...
متن کاملSome results on the partial orderings of block matrices
* Correspondence: [email protected] College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China Abstract Some results relating to the block matrix partial orderings and the submatrix partial orderings are given. Special attention is paid to the star ordering of a sum of two matrices and the minus ordering of matrix product. Several equivalent conditions for the min...
متن کاملSpace Decomposition and Partial Order on Matrices ∗
Motivated by the observation that there exists one-to-one correspondence between column space decompositions and row space decompositions of a matrix, the class of matrices dominated by this matrix under ‘≤’ is characterized in terms of characteristic of column space decompositions, where ≤ is a matrix partial order such as the star partial order, the sharp partial order, and the core partial o...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1999
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)10108-8