On the matrix function Ax+X′A′

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1962 English Publisher:Springer Science and Business Media LLCJournal:Archive for Rational Mechanics and Analysis, volume 9, pages 93-96 (issn: 0003-9527, eissn: 1432-0673,

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Authors: Taussky, O.; Wielandt, Helmut;

doi: 10.1007/bf00253335

On the matrix function Ax+X′A′

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Abstract

Proof. Let ~ denote the space of all ant isymmetric n x n matrices with elements in F. The space ~ has dimension n(n--1)/2, and, since char F=~2, we have 6 ~ = { 0 } . Hence 6 and ~ together span the whole linear space ~. Choose a basis B x . . . . . 13,, of ~ such that B x . . . . . B~r are in 6 , and BN+ 1 . . . . . B, , are in ~. With respect to this basis (ordered in a row) the matr ix of g has the form

Related Organizations

California Institute of Technology
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University of Tübingen
Germany

Keywords

linear algebra, polynomials, forms, invariants

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