Density of diagonalizable matrices in sets of structured matrices defined from indefinite scalar products

2020/07/01 by de la Cruz, Ralph John, Saltenberger, Philip
#FOS: Mathematics #Numerical Analysis (math.NA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2007.00269

Abstract

For an (indefinite) scalar product [x,y]_B = x^HBy for B= ± B^H ∈ Gl_n(ℂ) on ℂⁿ × ℂⁿ we show that the set of diagonalizable matrices is dense in the set of all B-selfadjoint, B-skewadjoint, B-unitary and B-normal matrices.

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