Linear Algebra

Characteristic equation - good

solve det(A-λI) = 0 to find the characteristic equation for A; shows all possible values of λ. Expand for polynomial.
Let A be an n x n matrix. A is invertible iff:
a. The number 0 is not an eigenvalue of A
b. the determinant of A is not zero.

Dunno if it helps to point out why these conditions are equivalent - since you're solving for det(A-λI) = 0, iff 0 is an eigenvalue then you know det(A-0) = 0. And invertibility has A*A^-1 = I, so det(A) * det(A^-1) = 1. If either of those is 0 the other's undefined since det(A^-1) = 1/0.

I just find it easier to remember stuff based on quick explanations of where it comes from than by rote. If I remember a proof wrong then a step becomes illogical; if I remember a sentence wrong it's hard to tell.