In terms of programming and linear algebra - please consult someone who is actually knowledgeable about the subject if you're implementing it in code.

Linear algebra without error analysis is very dangerous. Many many things are theoretically useful, but can't be used in practice. You can't calculate determinants, you can't count unique eigen values, you can't use certain decompositions.

Unfortunately this isn't really topic you can do a quick tutorial on and start writing new algorithms