A non-holomorphic functional calculus and the complex conjugate of a matrix

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Based on Stokes' theorem we derive a non-holomorphic functional calculus for matrices, assuming sufficient smoothness near eigenvalues, corresponding to the size of related Jordan blocks. It is then applied to the complex conjugation function τ:z↦z‾. The resulting matrix agrees with the hermitian transpose if and only if the matrix is normal. Two other, as such elementary, approaches to define the complex conjugate of a matrix yield the same result.


Original languageEnglish
Pages (from-to)191-220
Number of pages30
JournalLinear Algebra and Its Applications
Publication statusPublished - 15 Jan 2018
MoE publication typeA1 Journal article-refereed

    Research areas

  • Functional calculus, Non-holomorphic, Nondiagonalizable matrices

ID: 29743940