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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Golan, J.S. (2012). The Algebra of Square Matrices. In: The Linear Algebra a Beginning Graduate Student Ought to Know. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2636-9_9
Download citation
DOI: https://doi.org/10.1007/978-94-007-2636-9_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-2635-2
Online ISBN: 978-94-007-2636-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)