>>13540013the first thing you should absolutely do is take Hoffman and Kunze and read Chapters 4&5, on polynomials and determinants, respectively. determinants are important and as good as Axler is he does not do them justice AT ALL. i'd also recommend reading the chapters on inner product spaces and bilinear forms
afterwards, if you want even MORE LA read either something that dives deep into theory (maybe Roman or Greub) or try matrix stuff (Horn&Johnson for example)