| The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I￡ogroups, rings, fields, homomorphisms, is presup-posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume.References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any 'student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. 此书为英文版！ |
| CHAPTER I￡oFINITE DIMENSIONAL VECTOR SPACES SECTION 1. Abstract vector spaces 2. Right vector spaces 3. o-modules 4. Linear dependence S. Invariance of dimensionality 6. Bases and matrices 7. Applications to matrix theory 8. Rank of a set of vectors 9. Factor spaces 10. Algebra of subspaces 11. Independent subspaces, direct sums CHAPTER II￡oLINEAR TRANSFORMATIONS 1 ￡?Definition and examples 2. Compositions of linear transformations 3 ￡?The matrix of a linear transformation 4. Compositions of matrices 5. Change of basis. Equivalence and similarity of matrices 6. Rank space and null space of a linear transformation￡? 7. Systems of linear equations 8. Linear transformations in right vector spaces 9. Linear functions 10. Duality between a finite dimensional space and its conjugate space 11. Transpose of a linear transformation 12. Matrices of the transpose 13. Projections CHAPTER III￡oTHE THEORY OF A SINGLE LINEAR TRANSFORMATION 1. The minimum polynomial of a linear transformation 2. Cyclic subspaces …… |
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