Linear algebra [electronic resource]

• 作者： Liesen, Jorg.
• 其他作者：
  • Mehrmann, Volker.
  • SpringerLink (Online service)
• 其他題名：
  • Springer undergraduate mathematics series
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Springer undergraduate mathematics series
• 主題： Algebras, Linear , Mathematics , Matrix theory. , Algebra , Linear and Multilinear Algebras, Matrix Theory.
• ISBN： 9783319243467 (electronic bk.) 、 9783319243443 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
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• 摘要註: 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 book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several 'MATLAB-Minutes' students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.
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