# Math 4326 Linear Algebra

Major Theorems for Final Exam

## Spring 2008

One of these three theorems will appear on the final exam for you to give the proof of:
**3.4**: dim *V* = dim null *T* + dim range *T*
**5.13**: In a complex vector space, for every linear
transformation there is a basis such that the corresponding matrix is
upper-triangular. You will also be responsible for memorizing the
statement (but not proof) of 5.12, some technical descriptions of an
upper-triangular matrix.
**6.20/6.24**: Gram-Schmidt and the existence of orthonormal bases in an inner-product space.

[Note: These statements are just quick, imprecise summaries of each result.]