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arXiv · 2212.10966

Fast multiplication, determinants, and inverses of arrowhead and diagonal-plus-rank-one matrices over associative fields

Nevena Jakovcevic Stor·Ivan Slapnicar
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Abstract

The article considers arrowhead and diagonal-plus-rank-one matrices in F^(nxn) where F in R,C or H. H is a non-commutative field of quaternions. We give unified formulas for fast matrix-vector multiplications, determinants, and inverses for considered matrices. The formulas are unified in the sense that the same formula holds in both, commutative and noncommutative algebras. Each formula requires O(n) arithmetic operations. Most of the formulas hold for block matrices, as well.

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Nevena Jakovcevic Stor, Ivan Slapnicar. 2022-12-21. Fast multiplication, determinants, and inverses of arrowhead and diagonal-plus-rank-one matrices over associative fields. https://arxiv.org/abs/2212.10966

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