Additive Decomposition of Real Matrices

Authors: Li C-K.¹; Poon E.¹

Source: Linear and Multilinear Algebra, Volume 50, Number 4, 1 January 2002 , pp. 321-326(6)

Publisher: Taylor and Francis Ltd

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Abstract:

The orthogonal orbit ${cal O}(A)$ of an n×n real matrix A is the set of real matrices of the form $Pˆt AP$ where $Pˆt P = I_n$. We show that $A/ | A|$ is an affine sum of four orthogonal matrices, and note that $Aˆt$ can always be written as an affine combination of no more than 2n-1 matrices in ${cal O}(A)$. This improves some recent results of Zhan, and answers some of his questions. Other related results are also discussed.

Keywords: Orthogonal matrices; Orthogonal orbit

Document Type: Research article

Affiliations: 1: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187, USA

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