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. |
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Page iii
... theory of determinants will be found helpful. It is not easy to estimate what level of abstractness best suits a textbook of linear algebra. Since I have aimed, above all, at simplicity of presentation I have decided on a thoroughly ...
... theory of determinants will be found helpful. It is not easy to estimate what level of abstractness best suits a textbook of linear algebra. Since I have aimed, above all, at simplicity of presentation I have decided on a thoroughly ...
Page iv
... theory. I have also included a brief sketch of the theory of matrix power series, a topic of considerable interest and elegance not normally dealt with in elementary textbooks. Numerous exercises are incorporated in the text. They are ...
... theory. I have also included a brief sketch of the theory of matrix power series, a topic of considerable interest and elegance not normally dealt with in elementary textbooks. Numerous exercises are incorporated in the text. They are ...
Page vi
... 72 '74 78 85 87 90 97 100 111 113 123 126 VI. 5.3. The general theory of linear equations 5.4. Systems. 5.1. 5.2. Preliminary results The rank theorem 131 136 12.1. Operators and forms of the bilinear and quadratic types.
... 72 '74 78 85 87 90 97 100 111 113 123 126 VI. 5.3. The general theory of linear equations 5.4. Systems. 5.1. 5.2. Preliminary results The rank theorem 131 136 12.1. Operators and forms of the bilinear and quadratic types.
Page vii
... theory 6.4. Congruence transformations 6.5. The general concept of equivalence 6 .6. Axiomatic characterization of determinants PART II 140 148 152 158 168 172 178 182 186 189. FURTHER. DEVELOPMENT. OF. MATRIX. THEORY. VII. THE ...
... theory 6.4. Congruence transformations 6.5. The general concept of equivalence 6 .6. Axiomatic characterization of determinants PART II 140 148 152 158 168 172 178 182 186 189. FURTHER. DEVELOPMENT. OF. MATRIX. THEORY. VII. THE ...
Page 1
... theory of determinants, partly for theoretical purposes and partly as an aid to computation. In this opening chapter we shall develop the principal properties of determinants to the extent to which they are needed for the treatment of ...
... theory of determinants, partly for theoretical purposes and partly as an aid to computation. In this opening chapter we shall develop the principal properties of determinants to the extent to which they are needed for the treatment of ...
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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