An Introduction to Linear AlgebraCourier Corporation, 3 déc. 2012 - 464 pages "The straight-forward clarity of the writing is admirable." — American Mathematical Monthly. This work provides an elementary and easily readable account of linear algebra, in which the exposition is sufficiently simple to make it equally useful to readers whose principal interests lie in the fields of physics or technology. The account is self-contained, and the reader is not assumed to have any previous knowledge of linear algebra. Although its accessibility makes it suitable for non-mathematicians, Professor Mirsky's book is nevertheless a systematic and rigorous development of the subject. Part I deals with determinants, vector spaces, matrices, linear equations, and the representation of linear operators by matrices. Part II begins with the introduction of the characteristic equation and goes on to discuss unitary matrices, linear groups, functions of matrices, and diagonal and triangular canonical forms. Part II is concerned with quadratic forms and related concepts. Applications to geometry are stressed throughout; and such topics as rotation, reduction of quadrics to principal axes, and classification of quadrics are treated in some detail. An account of most of the elementary inequalities arising in the theory of matrices is also included. Among the most valuable features of the book are the numerous examples and problems at the end of each chapter, carefully selected to clarify points made in the text. |
À l'intérieur du livre
Résultats 1-5 sur 87
Page v
... linear algebra and their presentation to students. But for these conversations I should not have been able to write the book. Dr. Kneebone has also read and criticized the manuscript at every stage of ... LINEAR EQUATIONS I. PREFACE v.
... linear algebra and their presentation to students. But for these conversations I should not have been able to write the book. Dr. Kneebone has also read and criticized the manuscript at every stage of ... LINEAR EQUATIONS I. PREFACE v.
Page vi
... linear equations VECTOR SPACES AND LINEAR MANIFOLDS 2.1. 2.2. 2.3. 2.4. 2.5. The algebra of vectors Linear manifolds Linear dependence and bases Vector representation of linear manifolds Inner products and orthonormal bases III. THE ...
... linear equations VECTOR SPACES AND LINEAR MANIFOLDS 2.1. 2.2. 2.3. 2.4. 2.5. The algebra of vectors Linear manifolds Linear dependence and bases Vector representation of linear manifolds Inner products and orthonormal bases III. THE ...
Page vii
L. Mirsky. VI. 5.3. The general theory of linear equations 5.4. Systems of homogeneous linear equations 5.5. Miscellaneous applications 5.6. Further theorems on rank of matrices ELEMENTARY OPERATIONS AND THE CONCEPT OF EQUIVALENCE 6.1. E ...
L. Mirsky. VI. 5.3. The general theory of linear equations 5.4. Systems of homogeneous linear equations 5.5. Miscellaneous applications 5.6. Further theorems on rank of matrices ELEMENTARY OPERATIONS AND THE CONCEPT OF EQUIVALENCE 6.1. E ...
Page viii
... linear differential equations. PART. III. QUADRATIC. FORMS. XII. BILINEAR, QUADRATIC, AND HERMITIAN FORMS 306 312 316 327 330 341 343 PART I DETERMINANTS, VECTORS, MATRICES, AND LINEAR EQUATIONS I DETERMINANTS. 12.1. Operators and forms of ...
... linear differential equations. PART. III. QUADRATIC. FORMS. XII. BILINEAR, QUADRATIC, AND HERMITIAN FORMS 306 312 316 327 330 341 343 PART I DETERMINANTS, VECTORS, MATRICES, AND LINEAR EQUATIONS I DETERMINANTS. 12.1. Operators and forms of ...
Page 1
L. Mirsky. PART I DETERMINANTS, VECTORS, MATRICES, AND LINEAR EQUATIONS I DETERMINANTS THE present book is intended to give a systematic account of the elementary parts of linear algebra. The technique best suited to this branch of ...
L. Mirsky. PART I DETERMINANTS, VECTORS, MATRICES, AND LINEAR EQUATIONS I DETERMINANTS THE present book is intended to give a systematic account of the elementary parts of linear algebra. The technique best suited to this branch of ...
Autres éditions - Tout afficher
Expressions et termes fréquents
A₁ algebra assertion automorphism b₁ basis bilinear form bilinear operator canonical forms characteristic roots characteristic vectors coefficients columns commute complex numbers convergent coordinates Deduce defined denote determinant diagonal form diagonal matrix dimensionality E-operations edition equal equivalence EXERCISE exists follows functions geometry given Hence hermitian form hermitian matrix identity implies inequality integers invariant space isomorphic linear equations linear manifold linear transformation linearly independent matrix group minimum polynomial multiplication non-singular linear transformation non-singular matrix non-zero numbers nxn matrix obtain orthogonal matrix positive definite positive semi-definite possesses problems proof of Theorem prove quadratic form quadric rank relation represented respect result rotation S-¹AS satisfies scalar Show similar singular skew-symmetric matrix solution square matrix suppose symmetric matrix t₁ theory tions triangular unique unit element unitary matrix values vector space view of Theorem write x₁ xTAx y₁ zero