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Miscalculated Eigen Vectors


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#1 aacs88

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Posted 26 November 2007 - 01:55 AM

I surprised a lot qhe i put the following matrix

68.75 0 0
0 68.75 0
0 0 0

I executed the eigVc command and I obtained

1 0.707 0
0 -0707 0
0 0 1

I almost died when i saw this!!!
How can I fix this???
PS: If u dont realize...the first column is not ortogonal with 2nd column....its suppused that i should get the ijk vector system....

#2 aacs88

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Posted 28 November 2007 - 02:58 AM

please answer

!!!!

#3 Orwell

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Posted 01 December 2007 - 10:57 AM

On my classpad it gives
0 1 0
1 0 0
0 0 1

which is normal because your matrix is already diagonal.

#4 aacs88

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Posted 02 December 2007 - 12:39 PM

so there is a problem with my class pad
what can i do?

#5 Guest_Guest_*

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Posted 01 April 2008 - 01:20 AM

Plz i still dont get any answers

#6 Behnoud

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Posted 01 April 2008 - 09:35 AM

Do you use OS (Operating System) ver. 2.2?

#7 ECE

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Posted 01 April 2008 - 08:26 PM

I surprised a lot qhe i put the following matrix

68.75 0 0
0 68.75 0
0 0 0

I executed the eigVc command and I obtained

1 0.707 0
0 -0707 0
0 0 1

I almost died when i saw this!!!
How can I fix this???
PS: If u dont realize...the first column is not ortogonal with 2nd column....its suppused that i should get the ijk vector system....


aacs88:

Definition: let A be a square matrix and k is the eigenvalue of A if there exist nonzero vector P such that AP=kP . every nonzero vector P is called eigenvector of A associated with the eigenvalue k. this implies that both side are parallel vectors.

According to this definition your answer is correct. Since your eigenvalue are

k1 =68.75

k2=68.75

k3=0

then

|68.75 0 0||1| |1|

|0 68.75 0||0|= k1 |0|

|0 0 0||0| |0|

also

|68.75 0 0||0.707 | |0.707 |

|0 68.75 0||-0.707 |=k2 |-0.707|

|0 0 0| | 0 | | 0 |

And

|68.75 0 0||0| |0|

|0 68.75 0||0|= k3 |0|

|0 0 0||1| |1|

Notice that these eigenvectors are not unique i.e. there are infinitely many possible solutions as long as they satisfy AP=kP.

|0 1 0|

|1 0 0| is also a possible solution

|0 0 1|

The eigenvectors are not necessarily orthogonal, for your case you have a repeated eigenvalues in the diagonal matrix.



On my classpad it gives
0 1 0
1 0 0
0 0 1

which is normal because your matrix is already diagonal.


Orwell:

I've tried to solve this problem with my CP it gave me the answer

1 0.707 0

0 -0.707 0

0 0 0

I'm running OS v3.03, what method did you use to calculate the eigenvectors ?

Inform me please.

#8 Guest_Zwei9_*

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Posted 10 April 2008 - 11:41 PM

On an AFX 2.0+ I got the EigenVectors

1 1 0
0 0 0
0 0 1

for the EigenValues

68.75 68.75 0

Just my two cents :)




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