There are literally hundreds of introductory books on linear operators and their use in quantum mechanics. Finding the right one for you can be tricky. Let me recommend two that have been successful enough to be republished as Dover paperbacks. They're both by Thomas F. Jordan and are specifically oriented towards quantum mechanics applications. The most elementary one (perhaps too elementary) is,

"Quantum Mechanics in Simple Matrix Form" (1986) Dover (2005) ISBN 0-486-44530-5

The other one, significantly more sophisticated, but still very accessible is,

"Linear Operators for Quantum Mechanics" (1997) Dover (2006) ISBN 0-486-45329-4