## Find a copy online

### Links to this item

## Find a copy in the library

Finding libraries that hold this item...

## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
L Mirsky |

ISBN: | 1306390818 9781306390811 9780486166445 0486166449 |

OCLC Number: | 869522415 |

Description: | 1 online resource |

Contents: | 3.1. Elementary algebra3.2. Preliminary notions concerning matrices; 3.3. Addition and multiplication of matrices; 3.4. Application of matrix technique to linear substitutions; 3.5. Adjugate matrices; 3.6. Inverse matrices; 3.7. Rational functions of a square matrix; 3.8. Partitioned matrices; IV -- LINEAR OPERATORS; 4.1. Change of basis in a linear manifold; 4.2. Linear operators and their representations; 4.3. Isomorphisms and automorphisms of linear manifolds; 4.4. Further instances of linear operators; V -- SYSTEMS OF LINEAR EQUATIONS AND RANK OF MATRICES; 5.1. Preliminary results. 5.2. The rank theorem5.3. 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; VI -- ELEMENTARY OPERATIONS AND THE CONCEPT OF EQUIVALENCE; 6.1. E-operations and E-matrices; 6.2. Equivalent matrices; 6.3. Applications of the preceding theory; 6.4. Congruence transformations; 6.5. The general concept of equivalence; 6.6. Axiomatic characterization of determinants; PART II -- FURTHER DEVELOPMENT OF MATRIX THEORY; VII -- THE CHARACTERISTIC EQUATION. 7.1. The coefficients of the characteristic polynomial7.2. Characteristic polynomials and similarity transformations; 7.3. Characteristic roots of rational functions of matrices; 7.4. The minimum polynomial and the theorem of Cayley and Hamilton; 7.5. Estimates of characteristic roots; 7.6. Characteristic vectors; VIII -- ORTHOGONAL AND UNITARY MATRICES; 8.1. Orthogonal matrices; 8.2. Unitary matrices; 8.3. Rotations in the plane; 8.4. Rotations in space; IX -- GROUPS; 9.1. The axioms of group theory; 9.2. Matrix groups and operator groups; 9.3. Representation of groups by matrices. 9.4. Groups of singular matrices9.5. Invariant spaces and groups of linear transformations; X -- CANONICAL FORMS; 10.1. The idea of a canonical form; 10.2. Diagonal canonical forms under the similarity group; 10.3. Diagonal canonical forms under the orthogonal similarity group and the unitary similarity group; 10.4. Triangular canonical forms; 10.5. An intermediate canonical form; 10.6. Simultaneous similarity transformations; XI -- MATRIX ANALYSIS; 11.1. Convergent matrix sequences; 11.2. Power series and matrix functions; 11.3. The relation between matrix functions and matrix polynomials. |

### Abstract:

"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.

## Reviews

*User-contributed reviews*

Add a review and share your thoughts with other readers.
Be the first.

Add a review and share your thoughts with other readers.
Be the first.

## Tags

Add tags for "Introduction to Linear Algebra.".
Be the first.