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<p>In this paper we use the power of the outer exponential <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="6_2025_1407_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Lambda ^B\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Λ</mi> <mi>B</mi> </msup> </math></EquationSource> </InlineEquation> of a bivector <i>B</i> to see the so-called invariant decomposition from a different perspective. This is deeply connected with the eigenvalues for the adjoint action of <i>B</i>,&#xa0; a fact that allows a version of the Cayley–Hamilton theorem which factorises the classical theorem (both the matrix version and the geometric algebra version).</p>

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Outer and Eigen: Tangent Concepts

  • 期刊论文

  • 发表日期：

    2025年10月14日

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  • David Eelbode,
  • Martin Roelfs,
  • Steven De Keninck

摘要

In this paper we use the power of the outer exponential \(\Lambda ^B\) Λ B of a bivector B to see the so-called invariant decomposition from a different perspective. This is deeply connected with the eigenvalues for the adjoint action of B,  a fact that allows a version of the Cayley–Hamilton theorem which factorises the classical theorem (both the matrix version and the geometric algebra version).