Quadratic Forms and Matrices
eBook - PDF

Quadratic Forms and Matrices

An Introductory Approach

  1. 174 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Quadratic Forms and Matrices

An Introductory Approach

Book details
Table of contents
Citations

About This Book

Quadratic Forms and Matrices: An Introductory Approach focuses on the principles, processes, methodologies, and approaches involved in the study of quadratic forms and matrices. The publication first offers information on the general theory of quadratic curves, including reduction to canonical form of the general equation of a quadratic curve, invariants and classification, reduction to canonical form of the equation of a quadratic curve with center at the origin, and transformation of coordinates in the plane. The text then examines the general theory of quadratic surfaces. Topics include transformation of rectangular coordinates in space; general deductions based on the formulas for the transformation of coordinates; reduction to canonical form of the equation of a quadric with center at the origin; and reduction to canonical form of the general equation of a quadric surface. The manuscript ponders on linear transformations and matrices, including reduction of a quadratic form to canonical form; reduction to canonical form of the matrix of a symmetric linear transformation of space; change of the matrix of a linear transformation due to a change of basis; and geometric meaning of the determinant of a linear transformation. The publication is a vital reference for researchers interested in the study of quadratic forms and matrices.

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Information

Publisher
Academic Press
Year
2014
ISBN
9781483267678
Topic
Mathematics
Subtopic
Algebra
Index
Mathematics

Table of contents

  1. Front Cover
  2. Quadratic Forms and Matrices: An Introductory Approach
  3. Copyright Page
  4. Table of Contents
  5. Preface
  6. Translator's Note
  7. CHAPTER 1. General Theory of Quadratic Curves
  8. CHAPTER 2. General Theory of Quadric Surfaces
  9. CHAPTER 3. Linear Transformations and Matrices
  10. APPENDIX I: Vectors. Operations on Vectors and Some of Their Properties
  11. APPENDIX II: Elements of the Theory of Determinants
  12. Subject Index