Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups
نویسندگان
چکیده
منابع مشابه
Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups
For any matrix automorphism group G associated with a bilinear or sesquilinear form, Mackey, Mackey, and Tisseur have recently shown that the matrix sign decomposition factors of A ∈ G also lie in G; moreover, the polar factors of A lie in G if the matrix of the underlying form is unitary. Groups satisfying the latter condition include the complex orthogonal, real and complex symplectic, and ps...
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The sign function of a square matrix was introduced by Roberts in 1971. We show that it is useful to regard S = sign(A) as being part of a matrix sign decomposition A = SN, where N = (A ) ’ 1/z This decomposition leads to . the new representation sign(A) = A(A2)-‘i2. Most results for the matrix sign decomposition have a counterpart for the polar decomposition A = UH, and vice versa. To illustra...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2004
ISSN: 0895-4798,1095-7162
DOI: 10.1137/s0895479803426644