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MAT244-2014F
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How to find the eigenvector and determine type, special case.
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Topic: How to find the eigenvector and determine type, special case. (Read 4658 times)
Sheng Zang
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How to find the eigenvector and determine type, special case.
«
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.
«
Last Edit: December 07, 2014, 02:36:36 PM by Sheng Zang
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Victor Ivrii
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Re: How to find the eigenvector and determine type, special case.
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Reply #1 on:
December 07, 2014, 02:29:43 PM »
your post is incomprehensible
How to find eigenvector? See Linear algebra course and Sections 7.1, 7.2 of our textbook
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Sheng Zang
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Re: How to find the eigenvector and determine type, special case.
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Reply #2 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?
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Victor Ivrii
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Re: How to find the eigenvector and determine type, special case.
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Reply #3 on:
December 07, 2014, 03:09:35 PM »
Except $(0,1)$ is not an eigenvector but a generalized e.v.
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Sheng Zang
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Re: How to find the eigenvector and determine type, special case.
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Reply #4 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)
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Victor Ivrii
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Re: How to find the eigenvector and determine type, special case.
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Reply #5 on:
December 07, 2014, 03:33:48 PM »
Improper node. See in Textbook. Forum is not a substitution for it
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MAT244-2014F
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MAT244 Math--Lectures
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How to find the eigenvector and determine type, special case.