The Algebra of Square Matrices

Jonathan S. Golan ()
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Jonathan S. Golan: University of Haifa, Dept. of Mathematics

Chapter 9 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 147-188 from Springer

Abstract: Abstract The algebra of square matrices with entries in a fixed associate algebra over a field are considered. Special classes of square matrices (diagonal, tridiagonal, upper triangular, symmetric, Vandermonde, etc.) are defined and their properties are identified. Nonsingular matrices are studied in detail and methods for identifying them and computing matrix inverses are presented. Computational methods for matrix manipulation, including the Strassen–Winograd algorithm and LU-decompositions are discussed.

Keywords: Diagonal Matrice; Nonsingular Matrix; Elementary Matrice; Block Form; Multiplicative Identity (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-94-007-2636-9_9

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