LEADER 03727nam 22004815 450 001 9910753399403321 005 20231028144144.0 010 $a3-031-41026-2 024 7 $a10.1007/978-3-031-41026-0 035 $a(CKB)5600000000764537 035 $a(MiAaPQ)EBC30883111 035 $a(Au-PeEL)EBL30883111 035 $a(DE-He213)978-3-031-41026-0 035 $a(PPN)272914460 035 $a(EXLCZ)995600000000764537 100 $a20231028d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLinear Algebra Done Right$b[electronic resource] /$fby Sheldon Axler 205 $a4th ed. 2024. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2024. 215 $a1 online resource (408 pages) 225 1 $aUndergraduate Texts in Mathematics,$x2197-5604 311 $a3-031-41025-4 327 $aPreface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces -- 2. Finite-Dimensional Vector Spaces -- 3. Linear Maps -- 4. Polynomials -- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces -- 6. Inner Product Spaces -- 7. Operators on Inner Product Spaces -- 8. Operators on Complex Vector Spaces -- 9. Operators on Real Vector Spaces -- 10. Trace and Determinant-Photo Credits-Symbol Index-Index. 330 $aNow available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. From reviews of previous editions: Altogether, the text is a didactic masterpiece. ? zbMATH The determinant-free proofs are elegant and intuitive. ? American Mathematical Monthly The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library ? CHOICE. 410 0$aUndergraduate Texts in Mathematics,$x2197-5604 606 $aAlgebras, Linear 606 $aLinear Algebra 615 0$aAlgebras, Linear. 615 14$aLinear Algebra. 676 $a512.5 700 $aAxler$b Sheldon$059614 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910753399403321 996 $aLinear Algebra done right$9374744 997 $aUNINA