With matrix multiplication, it's easier to start with the dot product between two vectors. Learn how it's a projection, how it's the cosine, how it's a test of similarity. Then do matrix vector multiplication, so the dot product repeated. So you're testing how much the vector is on the axes of a basis. Only then so matrix multiplication. Do it that way and it'll be clear why you're doing it. That way you won't just be memorising operations.
Well, LA does have many equally valid ways you can look at it. I like to look at it geometrically in column space with bases rather than just numbers you do operations on.
With matrix multiplication, it's easier to start with the dot product between two vectors. Learn how it's a projection, how it's the cosine, how it's a test of similarity.
Then do matrix vector multiplication, so the dot product repeated. So you're testing how much the vector is on the axes of a basis.
Only then so matrix multiplication.
Do it that way and it'll be clear why you're doing it. That way you won't just be memorising operations.
I appreciate the viewpoint. I’m following a textbook which doesn’t cover dot products until later.
Well, LA does have many equally valid ways you can look at it. I like to look at it geometrically in column space with bases rather than just numbers you do operations on.