This is a subject I struggled with the first time I took it. Ironically, this was the engineering version of it. It wasn't until I took the rigorous, axiomatic version that everything clicked.

tx and ty are translation. I think a and d are scale and b and c are some function of rotation. I have videos that are flipped and rotated using arbitrary matrices. How can I make them right-side-up ...

Vector spaces, linear transformation, matrix representation, inner product spaces, isometries, least squares, generalised inverse, eigen theory, quadratic forms, norms, numerical methods. The fourth ...