Matrix theory : from generalized inverses to Jordan form /: from generalized inverses to Jordan form. (2007)

• Record Type: Book
• Further Information: Note: Robert Piziak, P.L. Odell.
• Other Names: Piziak, Robert; Odell, Patrick L, 1930-
• Contents: THE IDEA OF INVERSE; Solving Systems of Linear Equations; The Special Case of "Square" Systems; ; GENERATING INVERTIBLE MATRICES; A Brief Review of Gauss Elimination with Back Substitution; Elementary Matrices; The LU and LDU Factorization; The Adjugate of a Matrix; The Frame Algorithm and the Cayley-Hamilton Theorem; ; SUBSPACES ASSOCIATED TO MATRICES; Fundamental Subspaces; A Deeper Look at Rank; Direct Sums and Idempotents; The Index of a Square Matrix; Left and Right Inverses; ; THE MOORE-PENROSE INVERSE; Row Reduced Echelon Form and Matrix Equivalence; The Hermite Echelon Form; Full Rank Factorization; The Moore-Penrose Inverse; Solving Systems of Linear Equations; Schur Complements Again; ; GENERALIZED INVERSES; The {1}-Inverse; {1, 2}-Inverses; Constructing Other Generalized Inverses; {2}-Inverses; The Drazin Inverse; The Group Inverse; ; NORMS; The Normed Linear Space Cn; Matrix Norms; ; INNER PRODUCTS; The Inner Product Space Cn; Orthogonal Sets of Vectors in Cn; QR Factorization; A Fundamental Theorem of Linear Algebra; Minimum Norm Solutions; Least Squares; ; PROJECTIONS; Orthogonal Projections; The Geometry of Subspaces and the Algebra of Projections; The Fundamental Projections of a Matrix; Full Rank Factorizations of Projections; Affine Projections; Quotient Spaces; ; SPECTRAL THEORY; Eigenstuff; The Spectral Theorem; The Square Root and Polar Decomposition Theorems; ; MATRIX DIAGONALIZATION; Diagonalization with Respect to Equivalence; Diagonalization with Respect to Similarity; Diagonalization with Respect to a Unitary; The Singular Value Decomposition; ; JORDAN CANONICAL FORM; Jordan Form and Generalized Eigenvectors; The Smith Normal Form; ; MULTILINEAR MATTERS; Bilinear Forms; Matrices Associated to Bilinear Forms; Orthogonality; Symmetric Bilinear Forms ; Congruence and Symmetric Matrices; Skew-Symmetric Bilinear Forms; Tensor Products of Matrices; ; APPENDIX A: COMPLEX NUMBERS; What is a Scalar?; The System of Complex Numbers; The Rules of Arithmetic in C; Complex Conjugation, Modulus, and Distance; The Polar Form of Complex Numbers; Polynomials over C; Postscript; ; APPENDIX B: BASIC MATRIX OPERATIONS; Introduction; Matrix Addition; Scalar Multiplication; Matrix Multiplication; Transpose; Submatrices; ; APPENDIX C: DETERMINANTS; Motivation; Defining Determinants; Some Theorems about Determinants; The Trace of a Square Matrix; ; APPENDIX D: A REVIEW OF BASICS; Spanning; Linear Independence; Basis and Dimension; Change of Basis; ; INDEX
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2007
• Extent: 1 online resource, illustrations
• Subjects: 512.9434; Matrices -- Textbooks; Algebras, Linear -- Textbooks; Matrix inversion -- Textbooks
• Languages: English
• ISBNs: 9781420009934; 1420009931
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.