# Toronto Math Forum

## MAT244-2014F => MAT244 Math--Lectures => Topic started by: Sheng Zang on December 07, 2014, 01:50:12 PM

Title: How to find the eigenvector and determine type, special case.
Post by: Sheng Zang on December 07, 2014, 01:50:12 PM
I got a question like this,
As I solved, I find the critical point is (0,0) and A= (0                 1)
(-6x^2+8     0)
after plug(0,0) into, it becomes (0, 1)
(0, 0)
so, Î»1=0=Î»2, how to solve eigenvector and determine the type of critical point?

Thanks for help.
Title: Re: How to find the eigenvector and determine type, special case.
Post by: Victor Ivrii on December 07, 2014, 02:29:43 PM

How to find eigenvector? See Linear algebra course and Sections 7.1, 7.2 of our textbook
Title: Re: How to find the eigenvector and determine type, special case.
Post by: Sheng Zang on December 07, 2014, 02:45:56 PM
I mean forÎ»1=0, matrix is A=(0 1)  *(x1) =(0)
(0 0)   (y1)    (0)
the eigenvector is (1,0) which is horizontal.

and since Î» is repeated, i.e Î»1=Î»2=0,
we solve (0 1)  *(x2) =(1)
(0 0)   (y2)    (0)
so, another eigenvector is (0,1), which is vertical.

Am I correct?
Title: Re: How to find the eigenvector and determine type, special case.
Post by: Victor Ivrii on December 07, 2014, 03:09:35 PM
Except $(0,1)$ is not an eigenvector but a generalized e.v.
Title: Re: How to find the eigenvector and determine type, special case.
Post by: Sheng Zang on December 07, 2014, 03:28:50 PM
Also what is the type of critical point?  proper or improper node? And how to draw pic?( I don't think this is as usual as we draw (im)proper node picture)
Title: Re: How to find the eigenvector and determine type, special case.
Post by: Victor Ivrii on December 07, 2014, 03:33:48 PM
Improper node. See in Textbook. Forum is not a substitution for it