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Abstract— <p>It is well known that if diagonalizable matrices <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12258_2025_280_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(A\)</EquationSource> <!--NumAnAp2503004Ikramov-m1--> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12258_2025_280_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(B\)</EquationSource> <!--NumAnAp2503004Ikramov-m2--> </InlineEquation> commute, then they can be brought to diagonal form by one and the same similarity transformation. We prove an analog of this assertion concerning nonsingular unitoid matrices and transformations of Hermitian congruence. A matrix is said to be unitoid if it can be brought to diagonal form by congruences.</p>

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Simultaneously Diagonalizable Matrices and the Congruence Analog of the Commutativity Property

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Kh. D. Ikramov

摘要

Abstract—

It is well known that if diagonalizable matrices \(A\) and \(B\) commute, then they can be brought to diagonal form by one and the same similarity transformation. We prove an analog of this assertion concerning nonsingular unitoid matrices and transformations of Hermitian congruence. A matrix is said to be unitoid if it can be brought to diagonal form by congruences.