I have been told that dsolve solves a second order differential equation by making two coupled first order equations.

Could someone please explain to me the reason that this is done?

I am getting the reecursive assignment error on the folowing code in the band[i]:= [band[]i[], ... section.

CreateMatrix is defined and I know that works and creates a global Matrix H

The process I am trying to do is create a new expanded Hermitian Matrix using one previosuly defined and then specifying the remaining elements of the upper triangle. This method works but wondering if the third line commands can be simplified into the one Matirx() command in the second line?

> HA := Matrix(2, {(1, 1) = 0, (1, 2) = f, (2, 2) = 0}, shape = hermitian);
> HAA := Matrix(4, HA, shape = hermitian);
> HAA(1, 3) := -t; HAA(2, 4) := -t; HAA(3, 4) := f;...