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Zusatztext Each chapter ends with a list of references for further reading. Undoubtedly! these will be useful for anyone who wishes to pursue the topics deeper. ? the book has many MATLAB examples and problems presented at appropriate places. ? the book will become a widely used classroom text for a second course on linear algebra. It can be used profitably by graduate and advanced level undergraduate students. It can also serve as an intermediate course for more advanced texts in matrix theory. This is a lucidly written book by two authors who have made many contributions to linear and multilinear algebra.-K.C. Sivakumar! IMAGE! No. 47! Fall 2011Always mathematically constructive! this book helps readers delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.-L'enseignement Mathématique! January-June 2007! Vol. 53! No. 1-2 Informationen zum Autor Piziak! Robert; Odell! P.L. Klappentext Suitable for the second-semester course in linear algebra! this work creates a bridge from linear algebra concepts to more advanced abstract algebra and matrix theory. It focuses on the development of the Moore-Penrose inverse. It provides MATLAB[registered] examples and exercises as well as homework problems and suggestions for further reading. Zusammenfassung Suitable for the second-semester course in linear algebra, this work creates a bridge from linear algebra concepts to more advanced abstract algebra and matrix theory. It focuses on the development of the Moore-Penrose inverse. It provides MATLAB[registered] examples and exercises as well as homework problems and suggestions for further reading. Inhaltsverzeichnis THE IDEA OF INVERSESolving Systems of Linear EquationsThe Special Case of "Square" SystemsGENERATING INVERTIBLE MATRICES A Brief Review of Gauss Elimination with Back SubstitutionElementary MatricesThe LU and LDU Factorization The Adjugate of a Matrix The Frame Algorithm and the Cayley-Hamilton TheoremSUBSPACES ASSOCIATED TO MATRICES Fundamental SubspacesA Deeper Look at RankDirect Sums and Idempotents The Index of a Square Matrix Left and Right InversesTHE MOORE-PENROSE INVERSE Row Reduced Echelon Form and Matrix EquivalenceThe Hermite Echelon FormFull Rank Factorization The Moore-Penrose Inverse Solving Systems of Linear EquationsSchur Complements Again GENERALIZED INVERSES The {1}-Inverse {1!2}-Inverses Constructing Other Generalized Inverses {2}-Inverses The Drazin Inverse The Group InverseNORMS The Normed Linear Space CnMatrix NormsINNER PRODUCTS The Inner Product Space CnOrthogonal Sets of Vectors in Cn QR FactorizationA Fundamental Theorem of Linear Algebra Minimum Norm Solutions Least SquaresPROJECTIONSOrthogonal ProjectionsThe Geometry of Subspaces and the Algebra of ProjectionsThe Fundamental Projections of a Matrix Full Rank Factorizations of ProjectionsAffine Projections Quotient SpacesSPECTRAL THEORYEigenstuff The Spectral TheoremThe Square Root and Polar Decomposition TheoremsMATRIX DIAGONALIZATION Diagonalization with Respect to EquivalenceDiagonalization with Respect to SimilarityDiagonalization with Respect to a UnitaryThe Singular Value DecompositionJORDAN CANONICAL FORM Jordan Form and Generalized EigenvectorsThe Smith Normal FormMULTILINEAR MATTERSBilinear FormsMatrices Associated to Bilinear FormsOrthogonality Symmetric Bilinear Forms Congruence and Symmetric Matrices Skew-Symmetric Bilinear FormsTensor Products of MatricesAPPENDIX A: COMPLEX NUMBERSWhat is a Scalar?The System of Complex Numbers The Rules of Arithmetic in CComplex Conjugation! Modulus! and Distance The Polar Form of Complex Numbers Polynomials over C PostscriptAPPENDIX B: BASIC MATRIX OPERATIONS IntroductionMatrix AdditionScalar MultiplicationMatrix MultiplicationTransposeSubmatricesAPPENDIX C: DETERMINANTS MotivationDefining Determinants Some Theorems about Determinants The Trace of a Square Ma...
