- #1
blondii
- 31
- 0
I have a matrix and can't seem to get my head around finding all the eigen vectors.
The matrix is A:
(1 0 0 0
1 0 0 1
0 1 0 0
0 0 1 0)
I got the eigen values as:
λ1 = 1, λ2 = λ3 = λ4 = 0
For λ1:
The eigen vector V1 is (0, 1, 1, 1).
For λ2 -> λ4:
The only eigen vector I could make out is: V2 (0, 0, 0, 0).
To calculate the remaining eigen vectors I solved for P using the formula (A-λI)P = K
Where K is an eigenvector of the matrix A associated with the eigenvalue (In this case V2). But substituting λ2 and V2 into the equation will only lead back again to the same equation which I don't think is correct. Is there a better method I can follow or is there something I am not doing correctly?
Thanks
The matrix is A:
(1 0 0 0
1 0 0 1
0 1 0 0
0 0 1 0)
I got the eigen values as:
λ1 = 1, λ2 = λ3 = λ4 = 0
For λ1:
The eigen vector V1 is (0, 1, 1, 1).
For λ2 -> λ4:
The only eigen vector I could make out is: V2 (0, 0, 0, 0).
To calculate the remaining eigen vectors I solved for P using the formula (A-λI)P = K
Where K is an eigenvector of the matrix A associated with the eigenvalue (In this case V2). But substituting λ2 and V2 into the equation will only lead back again to the same equation which I don't think is correct. Is there a better method I can follow or is there something I am not doing correctly?
Thanks