As an upcoming fourth year Math major, I'll be soon undertaking my thesis and it has been suggested to me by my supervisor that I read up on Unitary and Orthonormal groups.
I've studied a year of complex analysis (up to finding sums of certain series with residues and some naively seemingly random theorems), a year of abstract algebra (up to algebraic extensions), a year of linear algebra (the plug n' chug variety followed by the rigorous variety), and a semester of real analysis (up to Riemann Integration) along with extra reading of all of the above in my spare time. What are some good texts that would help me accomplish my goal of learning about these particular groups given my background?
To be specific, I will be applying this knowledge to the problem of finding eigenvalues of matrices so texts that related these groups to eigenvalues/eigenvectors would be even more useful to me.
Thanks in advance!