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.

翻译：文章考虑了F ⁇ (nxn)中的箭头和对角加一矩阵,其中F在R、C或H.H.中是一个非混合的四元字段。我们为快速矩阵-矢量乘法、决定因素和考虑的矩阵反向提供了统一的公式。公式是统一的,因为同一公式同时持有通量代数和非对流代数。每个公式都需要O(n)算术操作。大多数公式也持有区块矩阵。