- 224 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
An Introduction to the Theory of Canonical Matrices
About this book
Thorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory’s principal features — from definitions and fundamental properties of matrices to the practical applications of their reduction to canonical forms.
Beginning with matrix multiplication, reciprocals, and partitioned matrices, the text proceeds to elementary transformations and bilinear and quadratic forms. A discussion of the canonical reduction of equivalent matrices follows, including treatments of general linear transformations, equivalent matrices in a field, the H. C. F. process for polynomials, and Smith’s canonical form for equivalent matrices. Subsequent chapters treat subgroups of the group of equivalent transformations and collineatory groups, discussing both rational and classical canonical forms for the latter.
Examinations of the quadratic and Hermitian forms of congruent and conjunctive transformative serve as preparation for the methods of canonical reduction explored in the final chapters. These methods include canonical reduction by unitary and orthogonal transformation, canonical reduction of pencils of matrices using invariant factors, the theory of commutants, and the application of canonical forms to the solution of linear matrix equations. The final chapter demonstrates the application of canonical reductions to the determination of the maxima and minima of a real function, solving the equations of the vibrations of a dynamical system, and evaluating integrals occurring in statistics.
Beginning with matrix multiplication, reciprocals, and partitioned matrices, the text proceeds to elementary transformations and bilinear and quadratic forms. A discussion of the canonical reduction of equivalent matrices follows, including treatments of general linear transformations, equivalent matrices in a field, the H. C. F. process for polynomials, and Smith’s canonical form for equivalent matrices. Subsequent chapters treat subgroups of the group of equivalent transformations and collineatory groups, discussing both rational and classical canonical forms for the latter.
Examinations of the quadratic and Hermitian forms of congruent and conjunctive transformative serve as preparation for the methods of canonical reduction explored in the final chapters. These methods include canonical reduction by unitary and orthogonal transformation, canonical reduction of pencils of matrices using invariant factors, the theory of commutants, and the application of canonical forms to the solution of linear matrix equations. The final chapter demonstrates the application of canonical reductions to the determination of the maxima and minima of a real function, solving the equations of the vibrations of a dynamical system, and evaluating integrals occurring in statistics.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access An Introduction to the Theory of Canonical Matrices by H. W. Turnbull,A. C. Aitken in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Cover
- Title Page
- Dedication Page
- Copyright page
- Preface
- Preface to the Second Impression
- Preface to the Third Impression
- Contents
- Chapter I: Definitions and Fundamental Properties of Matrices
- Chapter II: Elementary Transformations. Bilinear and Quadratic Forms
- Chapter III: The Canonical Reduction of Equivalent Matrices
- Chapter IV: Subgroups of the Group of Equivalent Transformations
- Chapter V: A Rational Canonical form for the Collineatory Group
- Chapter VI: The Classical Canonical form for the Collineatory Group
- Chapter VII: Congruent and Conjunctive Transformations: Quadratic and Hermitian Forms
- Chapter VIII: Canonical Reduction by Unitary and Orthogonal Transformations
- Chapter IX: The Canonical Reduction of Pencils of Matrices
- Chapter X: Applications of Canonical Forms to Solution of Linear Matrix Equations. Commutants and Invariants
- Chapter XI: Practical Applications of Canonical Reduction
- Appendix
- Miscellaneous Examples
- Index