内容提要 数学 目录 CHAPTER I: FINITE DIMENSIONAL VECTOR SPACES SECTION 1. Abstract vector spaces 2. Right vector spaces 3. o-modules'. 4. Linear dependence 5. Invariance of dimensionality 6. Bases and matrices 7. Applications to matrix theory 8. Rank of a set of vectors 9. Factor spaces I0. Algebra of subspaces 11. Independent subspaces, direct sums . . .
CHAPTER II: LINEAR TRANSFORMATIONS 1. Definition and examples 2. Compositions of linear transformations 3. The matrix of a linear transformatio 4. Compositions of matrices 5. Change of basis. Equivalence and similarity of matrices 6. Rank space and null space of a linear transformatio 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 transformatio 12. Matrices of the transpose 13. Projections CHAPTER III: THE THEORY OF A SINGLE LINEAR TRANSFORMATION 1. The minimum polynomial of a linear transformatio 2. Cyclic subspaces …… 作者介绍
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