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.
Original language | English |
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Pages (from-to) | 191-220 |
Number of pages | 30 |
Journal | Linear Algebra and Its Applications |
Volume | 537 |
DOIs | |
Publication status | Published - 15 Jan 2018 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Functional calculus
- Non-holomorphic
- Nondiagonalizable matrices