For another take on the "computer science" approach to QM, check out Chapter 9 in my book on linear algebra: https://minireference.com/static/tmp/quantum_chapter_excerpt...

I think it's important to understand linear algebra before doing matrix quantum mechanics, this way you can focus on learning the new quantum concepts and understand we are just using vectors and matrices as representations for them.

  - quantum state = vector
  - quantum gate = unitary matrix
  - quantum measurement = set of projection matrices that add to the identity

My book only covers very basic QM—not a full course by any means. For anyone interested in getting into quantum computing, I recommend Thomas G. Wong's book Introduction to Classical and Quantum Computing which you can find here https://www.thomaswong.net/#textbook or Nielsen and Chuang which is a classic.