TITLE: What is the difference between matrix theory and linear algebra?
QUESTION [13 upvotes]: Hi,
Currently, I'm taking matrix theory, and our textbook is Strang's Linear Algebra. Besides matrix theory, which all engineers must take, there exists linear algebra I and II for math majors. What is the difference,if any, between matrix theory and linear algebra?
Thanks!

REPLY [6 votes]: I'm with Jon.  Matrices don't always appear as linear transformations.  Yes, you can look at them as linear transformations, but there are times when it's better not to and study them for their own right.  Jon already gave one example.  Another example is the theory of positive (semi)definite matrices.  They appear naturally as covariance matrices of random vectors.  The notions like schur complements appear naturally in a course in matrix theory, but probably not in linear algebra.