2021/05/18 by L. Losonczi, Losonczi, L.
Computer Science · Engineering · #15A09 #15A15 #15B99 #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #Topological and Geometric Data Analysis #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2105.09775
openalex publication_date 2021/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let n,k be fixed natural numbers with 1≤ k≤ n and let An+1,k,2k,…,sk denote an (n+1)× (n+1) complex multidiagonal matrix having s=[n/k] sub- and superdiagonals at distances k,2k,…,sk from the main diagonal. We prove that the set MDn,k of all such multidiagonal matrices is closed under multiplication and powers with positive exponents. Moreover the subset of MDn,k consisting of all nonsingular matrices is closed under taking inverses and powers with negative exponents. In particular we obtain that the inverse of a nonsingular matrix An+1,k (called k-tridigonal) is in MDn,k, moreover if n+1≤ 2k then A-1n+1,k is also k-tridigonal. Using this fact we give an explicite formula for this inverse.