Linear Algebra, 5th Edition

2 Linear Transformations and Matrices

1. 2.1 Linear Transformations, Null spaces, and Ranges

2. 2.2 The Matrix Representation of a Linear Transformation

3. 2.3 Composition of Linear Transformations and Matrix Multiplication

4. 2.4 Invertibility and Isomorphisms

5. 2.5 The Change of Coordinate Matrix

6. 2.6* Dual Spaces

7. 2.7* Homogeneous Linear Differential Equations with Constant Coefficients

In Chapter 1, we developed the theory of abstract vector spaces in considerable detail. It is now natural to consider those functions defined on vector spaces that in some sense “preserve” the structure. These special functions are called linear transformations, and they abound in both pure and applied mathematics. In calculus, the operations of differentiation and ...