Thread: for a 2x2 matrix A, how do i classify the system given by X_n+1 = AX_n

for a 2x2 matrix how do i decide if the origin is: (attractor, repellor, saddle, stable focus, unstable focus, or a center)?

can you give examples?

Look at the eigenvalue of A. Are they real or non-real complex? Are the real parts positive or negative?

i know how to find real/complex eigenvalues and determine if the real part is +ve or -ve, but "which condition tells me what type of origin it is?"