I've always loved this particular intuition - I remember it being stressed a ton in this 3b1b video (which a lot of people have probably already seen), which really helped me build extra intuition as to why matrix multiplication could be useful in any sort of graphical context.
I also love the idea of the columns of the matrix being the basis vectors of the new space - just another neat trick to really help bring meaning to the numerical values.
I've always loved this particular intuition - I remember it being stressed a ton in this 3b1b video (which a lot of people have probably already seen), which really helped me build extra intuition as to why matrix multiplication could be useful in any sort of graphical context.
I also love the idea of the columns of the matrix being the basis vectors of the new space - just another neat trick to really help bring meaning to the numerical values.