If it seems weird to call a matrix a function, just remember that all matrices map input coordinates (i,j) to output values f(i,j). Matrices are functions that are just sparsely defined.

We can do better than that! An NxM matrix is a linear function from m-space to n-space; IE a 1x2 matrix maps points on a plane to points on a line. That’s why matrix multiplication looks so weird: it’s actually function composition.

(The post is good, I just like nerding out about linear algebra)

I did not do well in college physics, but shouldn’t any perfectly insulated heat plate with a heat source eventually converge to 1.0 everywhere? Without any heat sinks, shouldn’t it just keep getting hotter and hotter until it matches the temperature of the source?

I think so, but the examples used aren’t that – that would be equivalent to a Dirichlet condition where all the edges are pinned to 1. In the examples given, only 1 edge (the rightmost) is pinned to 1, and the other edges are all 0s, so there are sinks available (at least, that’s how I interpreted it).

We can do better than that! An NxM matrix is a linear function from m-space to n-space; IE a 1x2 matrix maps points on a plane to points on a line. That’s why matrix multiplication looks so weird: it’s actually function composition.

(The post is good, I just like nerding out about linear algebra)

I did not do well in college physics, but shouldn’t any perfectly insulated heat plate with a heat source eventually converge to 1.0 everywhere? Without any heat sinks, shouldn’t it just keep getting hotter and hotter until it matches the temperature of the source?

I think so, but the examples used aren’t that – that would be equivalent to a Dirichlet condition where all the edges are pinned to 1. In the examples given, only 1 edge (the rightmost) is pinned to 1, and the other edges are all 0s, so there are sinks available (at least, that’s how I interpreted it).

The Dirichlet example I agree makes sense. I was thinking more of the later examples where the 0 derivative edges are simulating a perfect insulator.