Matrixs

[leaden parcel]

Hello, I m just interested why is the multiplication so complicated?
I'm learning ML actually, and there are many times i should do that, although it is not evident.
Simply we could just cover one matrix by another, but we do a lot of strange things, mulipling columns rows etc.
Why is it necessairy? What is the difference between the way of multipllication I mentioned?

[leaden parcel]

And why exactly the right complicated way to muliply them is so beneficial?

[jaunty sigil]

it stems from the way linear transformations (which are represented by matrices) compose

[austere solstice]

yes

if A is the matrix of f, and B is the matrix of g, then AB is the matrix of f o g

in fact, if $B$ has columns $B_1, \ldots, B_n$, then $AB$ has columns $AB_1, \ldots, AB_n$

[viscid surge]

giovanni75

[austere solstice]

which is the way linear transformations work, they act on each vector of the chosen basis

[rough tendon]

I feel like the real substance is hidden in the "matrix-Vector multiplication what was defined earlier".
Not that this is bad. My answer would have been just to try it and other things and see what's useful. Though my other answer is that if M is the adjacency matrix of a graph, then a_ij in M^n is the number of paths of length n from i to j, which is my favourite mathematical fact.

[austere solstice]

the fact about graphs sounds really interesting