"Linear Algebra and its Applications"-chaper3-linear linear transformation

The two theorems are very simple, obviously, and seem to be the basic arithmetic in proving matrix algebra. But it lays a theoretical foundation for understanding Matrix-vector Product ax with "linear transformation".

Combining the properties of the matrix and vector product AX we discussed before, we can introduce a linear transformation.

Because the properties of the product of matrix A and vector x are closely related to the definition of linear transformation, we can further explore the role that matrix A plays in linear transformation.

With the concept of linear transformations and standard matrices, we have powerful tools to represent a series of linear transformations, such as stretching and scaling, in real-world problems.

"Linear Algebra and its Applications"-chaper3-linear linear transformation