Further Linear Algebra 1st edition by Thomas Blyth ISBN 1852334258 9781852334253

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Product details:

ISBN 10:      1852334258 
ISBN 13: 978-1852334253
Author:         Thomas S. Blyth

Further Linear Algebra 1st Table of contents:

1. Inner Product Spaces

   • Introduction to Inner Product Spaces
   • Properties and Applications
   • Examples and Theorems

2. Direct Sums of Subspaces

   • Definition and Properties of Direct Sums
   • Decompositions and Applications
   • Theorem on Direct Sums

3. Primary Decomposition

   • Primary Decomposition Theorem
   • Applications in Linear Algebra
   • Solving Problems Using Primary Decomposition

4. Reduction to Triangular Form

   • Concept of Triangular Forms
   • Procedures for Matrix Reduction
   • Practical Applications and Examples

5. Reduction to Jordan Form

   • Jordan Canonical Form Explained
   • Steps to Reduce Matrices to Jordan Form
   • Applications in Eigenvalues and Eigenvectors

6. Rational and Classical Forms

   • Rational Canonical Form
   • Classical Forms and Their Applications
   • Relationships between Forms

7. Dual Spaces

   • Definition of Dual Spaces
   • Properties and Theorems
   • Applications in Functional Analysis

8. Orthogonal Direct Sums

   • Orthogonality and Direct Sums
   • Orthogonal Projections and Decompositions
   • Applications in Geometry and Analysis

9. Bilinear and Quadratic Forms

   • Bilinear Forms and Properties
   • Quadratic Forms and Their Applications
   • Matrix Representation and Diagonalization

10. Real Normality

    • Concept of Real Normal Matrices
    • Normal Matrices and Their Diagonalization
    • Applications in Real Linear Algebra

11. Computer Assistance

    • Use of Computer Tools in Linear Algebra
    • Software for Matrix Computations
    • Practical Exercises and Algorithms

12. …. but Who Were They?

    • Historical Background and Key Figures in Linear Algebra
    • Contributions and Influence on the Field
    • Biographies and Key Works

13. Solutions to the Exercises

    • Detailed Solutions to Chapter Exercises
    • Step-by-Step Problem Solving
    • Explanation of Concepts and Methods
14.  

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