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  1. 1 Universitatis Iagellonicae Acta Mathematica

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  1. 1 2012

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  1. 1 Biborski I.

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On computation of skew-symmetric generator for an orthogonal matrix

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Biborski I.
Universitatis Iagellonicae Acta Mathematica
|
2012
|
vol. 50
47-51
EN
In this paper, we constructively prove that for any matrix $A$ over a field of characteristic $0$ and its eigenvalue $\lambda$ $\ne0$ there exists a diagonal matrix $D$ with diagonal coefficients $\pm$ $1$ such that $DA$ has no eigenvalue $\lambda$. Hence and by the canonical result on Cayley transformation, for each orthogonal matrix $U$ one can find a diagonal matrix $D$ and a skew-symmetric matrix $S$ such that $U=D (S−I)^{−1}$ $(S+I)$.
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