A non-holomorphic functional calculus and the complex conjugate of a matrix
Research output: Contribution to journal › Article › Scientific › peer-review
|Number of pages||30|
|Journal||Linear Algebra and Its Applications|
|Publication status||Published - 15 Jan 2018|
|MoE publication type||A1 Journal article-refereed|
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.
- Functional calculus, Non-holomorphic, Nondiagonalizable matrices