Research Catalog

Title

Matrix theory : from generalized inverses to Jordan form / Robert Piziak, P.L. Odell.

Author

Piziak, Robert.

Publication

Boca Raton : Chapman & Hall/CRC, c2007.

Items in the Library & Off-site

Holdings

Details

Additional Authors

Odell, Patrick L., 1930-2020

Description

xix, 548 p. : ill.; 24 cm.

Summary

"Highlighting the generalized inverse of a matrix and the method of full-rank factorization, Matrix Theory: From Generalized Inverses to Jordan Form probes introductory as well as more sophisticated linear algebra concepts. This presentation helps connect linear algebra to more advanced abstract algebra and matrix theory."--Jacket.

Series Statement

Monographs and textbooks in pure and applied mathematics

Uniform Title

Monographs and textbooks in pure and applied mathematics.

Subject

• Matrices > Textbooks
• Algebras, Linear > Textbooks
• Matrix inversion > Textbooks

Genre/Form

Textbooks

Bibliography (note)

• Includes bibliographical references and index.

Processing Action (note)

• committed to retain

Contents

• Idea of inverse -- Generating invertible matrices -- Subspaces associated to matrices. -- The Moore-Penrose inverse -- Generalized inverses -- Norms -- Inner products -- Projections -- Spectral theory -- Matrix diagonalization -- Jordan Canonical form -- Multilinear matters -- Appendix A: Complex numbers -- Appendix B: Basic matrix operations -- Appendix C: Determinants -- Appendix D: A review of basics.
• IDEA OF INVERSE Systems of Linear EquationsThe Special Case of "Square" SystemsGENERATING INVERTIBLE MATRICESA Brief Review of Gauss Elimination with Back SubstitutionElementary MatricesThe LU and LDU FactorizationThe Adjugate of a MatrixThe Frame Algorithm and the Cayley-Hamilton TheoremSUBSPACES ASSOCIATED TO MATRICESFundamental SubspacesA Deeper Look at RankDirect Sums and IdempotentsThe Index of a Square MatrixLeft and Right InversesTHE MOORE-PENROSE INVERSERow Reduced Echelon Form and Matrix EquivalenceThe Hermite Echelon FormFull Rank FactorizationThe Moore-Penrose InverseSolving Systems of Linear EquationsSchur Complements AgainGENERALIZED INVERSESThe {1}-Inverse{1,2}-InversesConstructing Other Generalized Inverses{2}-InversesThe Drazin InverseThe Group InverseNORMSThe Normed Linear Space CnMatrix NormsINNER PRODUCTSThe Inner Product Space CnOrthogonal Sets of Vectors in CnQR FactorizationA Fundamental Theorem of Linear AlgebraMinimum Norm SolutionsLeast^
• SquaresPROJECTIONSOrthogonal ProjectionsThe Geometry of Subspaces and the Algebra of ProjectionsThe Fundamental Projections of a MatrixFull Rank Factorizations of ProjectionsAffine ProjectionsQuotient SpacesSPECTRAL THEORYEigenstuffThe Spectral TheoremThe Square Root and Polar Decomposition TheoremsMATRIX DIAGONALIZATIONDiagonalization with Respect to EquivalenceDiagonalization with Respect to SimilarityDiagonalization with Respect to a UnitaryThe Singular Value DecompositionJORDAN CANONICAL FORMJordan Form and Generalized EigenvectorsThe Smith Normal FormMULTILINEAR MATTERSBilinear FormsMatrices Associated to Bilinear FormsOrthogonalitySymmetric Bilinear FormsCongruence and Symmetric MatricesSkew-Symmetric Bilinear FormsTensor Products of MatricesAPPENDIX A: COMPLEX NUMBERSWhat is a Scalar?The System of Complex NumbersThe Rules of Arithmetic in CComplex Conjugation, Modulus,^
• and DistanceThe Polar Form of Complex NumbersPolynomials over CPostscriptAPPENDIX B: BASIC MATRIX OPERATIONSIntroductionMatrix AdditionScalar MultiplicationMatrix MultiplicationTransposeSubmatricesAPPENDIX C: DETERMINANTSMotivationDefining DeterminantsSome Theorems about DeterminantsThe Trace of a Square MatrixAPPENDIX D: A REVIEW OF BASICSSpanningLinear IndependenceBasis and DimensionChange of BasisINDEX.

ISBN

• 9781584886259 (acid-free paper)
• 1584886250 (acid-free paper)

LCCN

^^2006025707

OCLC

• 70864476
• SCSB-10290904

Owning Institutions

Harvard Library