Urrutia, L. F.; Morales, N. The Cayley-Hamilton theorem for supermatrices. (English) Zbl 0834.15026 J. Phys. A, Math. Gen. 27, No. 6, 1981-1997 (1994). Summary: Starting from the expression for the superdeterminant of \((xI- M)\), where \(M\) is an arbitrary supermatrix, we propose a definition for the corresponding characteristic polynomial and we prove that each supermatrix satisfies its characteristic equation. Depending upon the factorization properties of the basic polynomials whose ratio defines the above-mentioned superdeterminant we are able to construct polynomials of lower degree which are also shown to be annihilated by the supermatrix. Some particular cases and examples are discussed. Cited in 1 ReviewCited in 3 Documents MSC: 15A75 Exterior algebra, Grassmann algebras 15A24 Matrix equations and identities 15A90 Applications of matrix theory to physics (MSC2000) 81T60 Supersymmetric field theories in quantum mechanics 83E99 Unified, higher-dimensional and super field theories Keywords:Grassmann algebra; Cayley-Hamilton matrix identity; superdeterminant; supermatrix; characteristic polynomial; characteristic equation Citations:Zbl 0777.15006; Zbl 0816.15027 PDFBibTeX XMLCite \textit{L. F. Urrutia} and \textit{N. Morales}, J. Phys. A, Math. Gen. 27, No. 6, 1981--1997 (1994; Zbl 0834.15026) Full Text: DOI arXiv