Dergiler / Fundamental journal of mathematics and applications (Online) / 2019 / Cilt: 2 - Sayı: 1

On Simultaneously and Approximately Simultaneously Diagonalizable $mathcal m$ -tuples of Matrices

On Simultaneously and Approximately Simultaneously Diagonalizable $mathcal m$ -tuples of Matrices

Maria Isabel GARCIA PLANAS

Sayfa
50–55
DOI
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Abstract

In this paper, the problem of simultaneous diagonalization of m-tuples of n-order squarecomplex matrices, is analyzed and some necessary and some necessary and sufficientconditions for this property to be fulfilled are presented. This study has an interest in itsapplications in different areas as for example in engineering and physical sciences. Forexample, they appear founding when we must give the instanton solution of Yang-Mills fieldpresented in an octonion form, and it can be represented by triples of traceless matrices.In the case where the m-tuple does not simultaneously diagonalize, the possibility of to findnear of the given m-tuple, an m-tuple that diagonalize simultaneously is studied.