Linear Algebra, 2e

Linear Algebra, 2e

Designed for undergraduate and postgraduate students of Mathematics, Linear Algebra, 2eexplains the basics comprehensively and with clarity. The flowing narrative of the book provides a refreshing approach to the subject. Drawing on decades of teaching experience and extensive discussions with teac...

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Detalles Bibliográficos
Autor principal: Saikia, Promode Kumar (-)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Noida : Pearson India 2014.
Edición:2nd ed
Materias:
Algebras, Linear > Textbooks.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009815723806719
Tabla de Contenidos:
  • Cover
  • Copyright
  • Contents
  • Preface
  • Preface to the Second Edition
  • A Note to Students
  • List of Symbols
  • Matrices
  • 1.1INTRODUCTION
  • 1.2BASIC CONCEPTS
  • 1.3 MATRIX OPERATIONS AND THEIR PROPERTIES
  • 1.4 INVERTIBLE MATRICES
  • 1.5 TRANSPOSE OF A MATRIX
  • 1.6 PARTITION OF MATRICES
  • BLOCK MULTIPLICATION
  • 1.7 GROUPS AND FIELDS
  • Systems of LinearEquations
  • 2.1 INTRODUCTION
  • 2.2 GAUSSIAN ELIMINATION
  • 2.3 ELEMENTARY ROW OPERATIONS
  • 2.4 ROW REDUCTION
  • 2.5 INVERTIBLE MATRICES AGAIN
  • 2.6 LU FACTORIZATION
  • 2.7 DETERMINANT
  • Vector Spaces
  • 3.1 INTRODUCTION
  • 3.2 BASIC CONCEPTS
  • 3.3 LINEAR INDEPENDENCE
  • 3.4 BASIS AND DIMENSION
  • 3.5 SUBSPACES AGAIN
  • 3.6 RANK OF A MATRIX
  • 3.7 ORTHOGONALITY IN Rn
  • 3.8 BASES OF SUBSPACES
  • 3.9 QUOTIENT SPACE
  • Linear Mapsand Matrices
  • 4.1 INTRODUCTION
  • 4.2 BASIC CONCEPTS
  • 4.3 ALGEBRA OF LINEAR MAPS
  • 4.4 ISOMORPHISM
  • 4.5 MATRICES OF LINEAR MAPS
  • Linear Operators
  • 5.1 INTRODUCTION
  • 5.2 POLYNOMIALS OVER FIELDS
  • 5.3 CHARACTERISTIC POLYNOMIALS AND EIGENVALUES
  • 5.4 MINIMAL POLYNOMIAL
  • 5.5 INVARIANT SUBSPACES
  • 5.6 SOME BASIC RESULTS
  • 5.7 REAL QUADRATIC FORMS
  • Canonical Forms
  • 6.1 INTRODUCTION
  • 6.2 PRIMARY DECOMPOSITION THEOREM
  • 6.3 JORDAN FORMS
  • Bilinear Forms
  • 7.1 INTRODUCTION
  • 7.2 BASIC CONCEPTS
  • 7.3 LINEAR FUNCTIONALS AND DUAL SPACE
  • 7.4 SYMMETRIC BILINEAR FORMS
  • 7.5 GROUPS PRESERVING BILINEAR FORMS
  • Inner Product Spaces
  • 8.1 INTRODUCTION
  • 8.2 HERMITIAN FORMS
  • 8.3 INNER PRODUCT SPACE
  • 8.4 GRAM-SCHMIDT ORTHOGONALIZATION PROCESS
  • 8.5 ADJOINTS
  • 8.6 UNITARY AND ORTHOGONAL OPERATORS
  • 8.7 NORMAL OPERATORS
  • Bibliography
  • Index
  • Blank Page.

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