Year: 2025
Type: article
Abstract: Let 𝐹 ∈ 𝑅, 𝐶, 𝐻 .Let 𝓤 𝒏×𝒏 be the set of secondary unitary bimatrics in 𝐹 𝑛 ×𝑛 , and let 𝑂 𝑛×𝑛 be the set of secondary orthogonal bimatrices in 𝐹 𝑛 ×𝑛 .Suppose 𝑛 ≥ 2, we show that every 𝐴 𝐵 ∈ 𝐹 𝑛×𝑛 can be written as a sum of bimatrices in 𝓤 𝒏×𝒏 and of bimatrices in 𝑂 𝑛×𝑛 .let 𝐴 𝐵 ∈ 𝐹 𝑛 ×𝑛 be given that and let 𝑘 ≥ 2 be the least integer that is a least upper bound of the singular values of A B .When F=R, we show that if 𝑘 ≤ 3, then A B can be written as a sum of 6 secondary orthogonal bimatrices; if 𝑘 ≥ 4, we show that A B can be written as a sum of 𝑘 + 2 secondary orthogonal bimatrices.
Authors: R. Surendar, M. Muthulakshmi
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4409210966