10 terms

real, different λs

both > 0

both > 0

repelling, unstable,

larger eigenvalue/vector pair dominates

larger eigenvalue/vector pair dominates

real, different λs

both < 0

both < 0

attractive, stable

largest absolute value of eigenvalue/vector pair dominates

largest absolute value of eigenvalue/vector pair dominates

real, different λs

λ1 > 0 , λ2 < 0

λ1 > 0 , λ2 < 0

saddle point

real, same λs

λ1 = λ2 > 0

2 eigenvectors

λ1 = λ2 > 0

2 eigenvectors

repelling

all pointing out

all pointing out

real, same λs

λ1 = λ2 < 0

2 eigenvectors

λ1 = λ2 < 0

2 eigenvectors

stable

all pointing in

all pointing in

real, same λs

λ1 = λ2 > 0

1 eigenvector

λ1 = λ2 > 0

1 eigenvector

repelling, unstable

(straight line, pushes away from center)

(straight line, pushes away from center)

real, same λs

λ1 = λ2 < 0

1 eigenvector

λ1 = λ2 < 0

1 eigenvector

attractive, stable

(straight line, pulls toward center)

(straight line, pulls toward center)

complex λ

real part = 0

real part = 0

marginally stable

rotating

concentric circles

rotating

concentric circles

complex λ

real part > 0

real part > 0

rotating, repelling

spiral outward

spiral outward

complex λ

real part < 0

real part < 0

rotating, attractive

spiral inward

spiral inward