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.]