抽象代数讲义 第2卷

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 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: THE THEORY OF A SINGLE LINEAR
TRANSFORMATION
 1. The minimum polynomial of a linear transformation
 2. Cyclic subspaces
　……