MAT244-2014F > TT2

TT2 # 4

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Victor Ivrii:
In the case of improper node one can also use clock-wise / counter-clock-wise criteria (sign of the top-right element in the matrix $A$).

Alex Hang:
So professor, since the top right element is positive, does that mean it has clockwise orientation, so shouldn't it be asymptotically stable?

Victor Ivrii:
Completely correct solution was provided by Shuyang Wang. Orientation and stability are different questions: stability follows from the sign of the eigenvalue ($r<0$; $r>0$ means instability) and orientation from the sign of the top-right element (which in the framework of the focal point/center/improper node opposite to the sign of the bottom-left)