Hate to do this, but it seems you just don't understand jack about linear algebra. I'm not even sure you read what I wrote.

1. Yes, I mixed in linear and non-linear processes. My point is that you use linear algebra even when working with non-linear processes.

2. Yes, I poo-pooed spreadsheets as a bad way to market linear algebra (I thought that was clear?)

3. Yes, I implied infinite dimensions is useful. Linear algebra in QM tends to be infinite-dimensional.

I'm reading a lot of hostility towards mathematics in general and linear algebra specifically (you've put a bunch of toxic comments all over this thread), and I'm not really sure why.