Once you get this, you can start building matrices for any (finite dimensional) 'vector space' not just the standard 'vectors as a list of numbers'.
All you need to do is to pick a basis for your vector space, and you can start to represent linear transformations as matrices w.r.t. that basis. Even cooler is when you let go of specific basis choices, and start talking about properties of linear transformations that do not depend on a choice of basis. Things like a determinant, eigenvalues, etc.
All you need to do is to pick a basis for your vector space, and you can start to represent linear transformations as matrices w.r.t. that basis. Even cooler is when you let go of specific basis choices, and start talking about properties of linear transformations that do not depend on a choice of basis. Things like a determinant, eigenvalues, etc.