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

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A non-holomorphic functional calculus and the complex conjugate of a matrix. / Nevanlinna, Olavi.

In: Linear Algebra and Its Applications, Vol. 537, 15.01.2018, p. 191-220.

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@article{a0a5074ff9e941caa244bbb829a91d12,
title = "A non-holomorphic functional calculus and the complex conjugate of a matrix",
abstract = "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.",
keywords = "Functional calculus, Non-holomorphic, Nondiagonalizable matrices",
author = "Olavi Nevanlinna",
year = "2018",
month = "1",
day = "15",
doi = "10.1016/j.laa.2017.10.004",
language = "English",
volume = "537",
pages = "191--220",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",

}

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TY - JOUR

T1 - A non-holomorphic functional calculus and the complex conjugate of a matrix

AU - Nevanlinna, Olavi

PY - 2018/1/15

Y1 - 2018/1/15

N2 - 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.

AB - 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.

KW - Functional calculus

KW - Non-holomorphic

KW - Nondiagonalizable matrices

UR - http://www.scopus.com/inward/record.url?scp=85030792517&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2017.10.004

DO - 10.1016/j.laa.2017.10.004

M3 - Article

VL - 537

SP - 191

EP - 220

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

ID: 29743940