LEADER 03835nam 2200589 450 001 9910483064203321 005 20230629004244.0 010 $a9783030528119 010 $a3-030-52811-1 024 7 $a10.1007/978-3-030-52811-9 035 $a(CKB)4100000011937975 035 $a(DE-He213)978-3-030-52811-9 035 $a(MiAaPQ)EBC6627984 035 $a(Au-PeEL)EBL6627984 035 $a(OCoLC)1252707509 035 $a(PPN)255885962 035 $a(EXLCZ)994100000011937975 100 $a20220124d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroduction to linear and matrix algebra$b[electronic resource] /$fNathaniel Johnston 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dŠ2021 215 $a1 online resource (XVI, 482 p. 324 illus., 286 illus. in color.) 311 $a3-030-52810-3 320 $aIncludes bibliographical references and index. 327 $aChapter 1: Vectors and Geometry -- Chapter 2: Linear systems and Subspaces -- Chapter 3: Unraveling Matrices -- Appendix A: Mathematical Preliminaries -- Appendix B: Additional Proofs -- Appendix C: Selected Exercises Solutions. 330 $aThis textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, ?Extra Topic? sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author?s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK. 606 $aAlgebra 606 $aAlgebras, Linear 606 $aMatrix theory 606 $aĀlgebra lineal$2thub 606 $aMatrius (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aAlgebra. 615 0$aAlgebras, Linear. 615 0$aMatrix theory. 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 $a9910483064203321 996 $aIntroduction to Linear and Matrix Algebra$91894209 997 $aUNINA