Matrix Representations
Matrix of a Linear Transformation
Change of Basis
Similarity
Properties
Examples
Example 1: defined by .
Relative to the standard basis:
Example 2: Differentiation .
Relative to basis :
Invariant Subspaces
Block Diagonal Form
If with each -invariant, then is block diagonal.
Coordinate Isomorphism
This is an isomorphism with .
Trace and Determinant
Characteristic Polynomial
The eigenvalues are the roots of .