Global Convergence of the $QR$ Algorithm for Unitary Matrices with Some Results for Normal Matrices

1975 ◽  
Vol 12 (1) ◽  
pp. 97-104 ◽  
Author(s):  
P. J. Eberlein ◽  
C. P. Huang
Keyword(s):  
Global Convergence ◽  
Unitary Matrices ◽  
Normal Matrices ◽  
Qr Algorithm

scholarly journals On the density of semisimple matrices in indefinite scalar product spaces

2021 ◽  
Vol 37 ◽  
pp. 387-401
Author(s):  
Ralph John De la Cruz ◽  
Philip Saltenberger
Keyword(s):  
Scalar Product ◽  
Product Spaces ◽  
Unitary Matrices ◽  
Analogous Statement ◽  
Normal Matrices

For an indefinite scalar product $[x,y]_B = x^HBy$ for $B= \pm B^H \in \mathbf{Gl}_n(\mathbb{C})$ on $\mathbb{C}^n \times \mathbb{C}^n$, it is shown that the set of diagonalizable matrices is dense in the set of all $B$-normal matrices. The analogous statement is also proven for the sets of $B$-selfadjoint, $B$-skewadjoint and $B$-unitary matrices.

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