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• W3039875189 abstract "Let $B$ be some invertible Hermitian or skew-Hermitian matrix. A matrix $A$ is called $B$-normal if $AA^star = A^star A$ holds for $A$ and its adjoint matrix $A^star := B^{-1}A^HB$. In addition, a matrix $Q$ is called $B$-unitary, if $Q^HBQ = B$. We develop sparse canonical forms for nondefective (i.e. diagonalizable) $J_{2n}$-normal matrices and $R_n$-normal matrices under $J_{2n}$-unitary ($R_n$-unitary, respectively) similarity transformations where $$J_{2n} = begin{bmatrix} & I_n - I_n & end{bmatrix} in M_{2n}(mathbb{C})$$ and $R_n$ is the $n times n$ sip matrix with ones on its anti-diagonal and zeros elsewhere. For both cases we show that these forms exist for an open and dense subset of $J_{2n}/R_n$-normal matrices. This implies that these forms can be seen as topologically 'generic' for $J_{2n}/R_n$-normal matrices since they exist for all such matrices except a nowhere dense subset." @default.
• W3039875189 created "2020-07-10" @default.
• W3039875189 creator A5038941411 @default.
• W3039875189 creator A5056406189 @default.
• W3039875189 date "2020-06-27" @default.
• W3039875189 modified "2023-09-27" @default.
• W3039875189 title "Generic canonical forms for perplectic and symplectic normal matrices." @default.
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• W3039875189 hasPublicationYear "2020" @default.
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