2024/01/04 by Ron Ofir, Ofir, Ron, Michael Margaliot +1 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Matrix Theory and Algorithms #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2401.02100
openalex publication_date 2024/01/04 · openalex created_date 2024/01/10 · openalex updated_date 2026/07/28
Compound matrices play an important role in many fields of mathematics and have recently found new applications in systems and control theory. However, the explicit formulas for these compounds are non-trivial and not always easy to use. Here, we derive new formulas for the multiplicative and additive compounds of a matrix using Kronecker products and sums. This provides a new approach to matrix compounds based on the well-known and powerful theory of Kronecker products and sums. We demonstrate several applications of these new formulas, including deriving a new expression for the additive compound of the product of two matrices.