# Math 4326 Linear Algebra

Major Theorems for Final Exam

## Spring 2015

One of these three theorems will appear on the final exam for you to give the proof of:
**5.27**: In a finite-dimensional 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 5.26, some technical descriptions of an
upper-triangular matrix.
**6.31/6.34**: Gram-Schmidt and the existence of orthonormal bases in an inner-product space.
**8.37**: Cayley-Hamilton theorem.

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