LEADER 03741nam 2200625 450 001 996466403803316 005 20230427102857.0 010 $a3-030-52815-4 024 7 $a10.1007/978-3-030-52815-7 035 $a(CKB)4100000011938300 035 $a(DE-He213)978-3-030-52815-7 035 $a(MiAaPQ)EBC6627983 035 $a(Au-PeEL)EBL6627983 035 $a(OCoLC)1252706564 035 $a(PPN)255885946 035 $a(EXLCZ)994100000011938300 100 $a20220124d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAdvanced linear and matrix algebra /$fNathaniel Johnston 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dŠ2021 215 $a1 online resource (XVI, 494 p. 123 illus., 108 illus. in color.) 311 $a3-030-52814-6 320 $aIncludes bibliographical references and index. 327 $aChapter 1: Vector Spaces -- Chapter 2: Matrix Decompositions -- Chapter 3: Tensors and Multilinearity -- Appendix A: Mathematical Preliminaries -- Appendix B: Additional Proofs -- Appendix C: Selected Exercise Solutions. 330 $aThis textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on concrete examples throughout, offering accessible pathways to advanced techniques. Beginning with a study of vector spaces that includes coordinates, isomorphisms, orthogonality, and projections, the book goes on to focus on matrix decompositions. Numerous decompositions are explored, including the Shur, spectral, singular value, and Jordan decompositions. In each case, the author ties the new technique back to familiar ones, to create a coherent set of tools. Tensors and multilinearity complete the book, with a study of the Kronecker product, multilinear transformations, and tensor products. Throughout, ?Extra Topic? sections augment the core content with a wide range of ideas and applications, from the QR and Cholesky decompositions, to matrix-valued linear maps and semidefinite programming. Exercises of all levels accompany each section. Advanced Linear and Matrix Algebra offers students of mathematics, data analysis, and beyond the essential tools and concepts needed for further study. The engaging color presentation and frequent marginal notes showcase the author?s visual approach. A first course in proof-based linear algebra is assumed. An ideal preparation can be found in the author?s companion volume, Introduction to Linear and Matrix Algebra. 606 $aAlgebras, Linear 606 $aMatrices 606 $aĀlgebra lineal$2thub 606 $aMatrius (Matemātica)$2thub 606 $aAlgebra 606 $aĀlgebra lineal$2thub 606 $aMatrius (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aAlgebras, Linear. 615 0$aMatrices. 615 7$aĀlgebra lineal 615 7$aMatrius (Matemātica) 615 0$aAlgebra. 615 7$aĀlgebra lineal 615 7$aMatrius (Matemātica) 676 $a512.5 700 $aJohnston$b Nathaniel$0848126 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466403803316 996 $aAdvanced Linear and Matrix Algebra$91896815 997 $aUNISA