Linear Algebra [electronic resource] by Jörg Liesen, Volker Mehrmann.

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This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the boo...

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Bibliographic Details
Uniform Title:Springer Undergraduate Mathematics Series, 2197-4144
Main Authors: Liesen, Jörg (Author)
Mehrmann, Volker (Author)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edition:1st ed. 2015.
Series:Springer Undergraduate Mathematics Series,
Subjects:
Algebras, Linear.
Online Access:
Springer English/International eBooks 2015 - Full Set: 2015 (Springer Link)
Format: Electronic eBook
Contents:
  • Linear Algebra in every day life
  • Basic mathematical concepts
  • Algebraic structures
  • Matrices
  • The echelon form and the rank of matrices
  • Linear systems of equations
  • Determinants of matrices
  • The characteristic polynomial and eigenvalues of matrices
  • Vector spaces
  • Linear maps
  • Linear forms and bilinear forms
  • Euclidean and unitary vector spaces
  • Adjoints of linear maps
  • Eigenvalues of endomorphisms
  • Polynomials and the Fundamental Theorem of Algebra
  • Cyclic subspaces, duality and the Jordan canonical form
  • Matrix functions and systems of differential equations
  • Special classes of endomorphisms
  • The singular value decomposition
  • The Kronecker product and linear matrix equations.