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- W4235526473 abstract "Chapter 4 Matrix Algebra Book Editor(s):Gérard Favier, Gérard FavierSearch for more papers by this author First published: 06 December 2019 https://doi.org/10.1002/9781119681137.ch4 AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onFacebookTwitterLinked InRedditWechat Summary This chapter presents an algebraic framework for the study of matrices and introduces bilinear/sesquilinear maps and bilinear/sesquilinear forms with their associated matrices. Having defined the main notations and a few special matrices, the chapter describes the transposition and vectorization operations. It then illustrates the notions of inner product, norm, and orthogonality in the case of Euclidean vectors. Next, the chapter considers matrix multiplication, including the definition of periodic, nilpotent, and idempotent matrices. It further defines matrix trace and Frobenius norm, and presents the fundamental subspaces associated with a matrix. Then, the notions of determinant, inverse, auto-inverse, and generalized inverse are described, along with the definition and a summary of the properties of the Moore–Penrose pseudo-inverse. The chapter also defines different structures of multiplicative groups of matrices. From Algebraic Structures to Tensors, Volume 1 RelatedInformation" @default.
- W4235526473 created "2022-05-12" @default.
- W4235526473 date "2019-12-06" @default.
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- W4235526473 title "Matrix Algebra" @default.
- W4235526473 doi "https://doi.org/10.1002/9781119681137.ch4" @default.
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