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- W4382363885 abstract "Let V be a finite-dimensional vector space over a field F, equipped with a symmetric or alternating non-degenerate bilinear form b. When the characteristic of F is not 2, we characterize the endomorphisms u of V that split into u=a1+a2 for some pair (a1,a2) of b-selfadjoint (respectively, b-skew-selfadjoint) endomorphisms of V such that (a1)2=(a2)2=0. In the characteristic 2 case, we obtain a similar classification for the endomorphisms of V that split into the sum of two square-zero b-alternating endomorphisms of V when b is alternating (an endomorphism v is called b-alternating whenever b(x,v(x))=0 for all x∈V). Finally, if the field F is equipped with a non-identity involution, we characterize the pairs (h,u) in which h is a Hermitian form on a finite-dimensional space over F, and u is the sum of two square-zero h-selfadjoint endomorphisms." @default.
- W4382363885 created "2023-06-29" @default.
- W4382363885 creator A5016953630 @default.
- W4382363885 date "2023-06-01" @default.
- W4382363885 modified "2023-10-17" @default.
- W4382363885 title "Sums of two square-zero selfadjoint or skew-selfadjoint endomorphisms" @default.
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- W4382363885 doi "https://doi.org/10.1016/j.laa.2023.06.020" @default.
- W4382363885 hasPublicationYear "2023" @default.
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