Linear Algebra 11L: The Three Equivalent Perspectives on Matrix Multiplication

[jamesspacer]

Easily the best maths lecturer on the Tube! Thank you so much! I've been learning Linear Algebra by just using a book - Elementary Linear Algebra by Andrilli and Hecker but it is so inefficient because it lacks the intuition part or maybe I'm just too stupid to take it the "pure" way. You are so good with the intuition and the different angles of view that I'm getting a much better perspective on the subject! Thanks again!!!

[griffinbur]

They're all important, but column perspective FTW because that is most closely related to the most intuitive geometric approach (IMHO): the child's definition of a vector x in R^2 is "over x1, up x2", and so we then say "well, what does over really mean" (I_1^t = [1, 0]) and "what does up really mean" (I_2^t = [0, 1]), so any vector is always already a product, just as any number is always already itself multiplied by one: any number or quantity is just "instructions" for stretching some base unit, and so is a vector: it's just "driving directions". Then, you can apply the driving directions to standard directions (canonical basis) or arbitrary, goofy ones (basically, most matrix multiplication). That's how I teach this as a extreme-non-mathematician, anyways.

[PaulA-krnl]

I think there’s a 4th perspective and that’s a block multiplication.