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Postby rinku.rohra85 » Wed Nov 27, 2013 3:33 pm

Can anyone explain me how to calculate normalized eigenvector.


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Postby yogesh » Thu Nov 28, 2013 11:28 am

If A is a square matrix, Eigen vector for A is some non zero vector v which when post multiplied by A gives a constant multiple of A i.e. A*v=K*v where K= non zero constant.
Usually to find Eigen vectors and Eigen values we first find Eigen values by using the characteristic polynomial i.e. Det(A-KI)=0 where K= non zero constant and I= identity matrix
Once we solve this we would get Eigen values and correspondingly we can find Eigen vectors.
Normalized Eigen vectors are Eigen vectors whose modulus is one.
A=|2 1| Find Eigen value and normalized Eigen vector for this matrix
|1 2|
Using the characteristic polynomial Det(A-KI)=0
(A-KI)= |2-K 1| Det(A-KI)=(2-K)*(2-K)-1*1=4+K^2-4K-1=0
|1 2-K| Thus, we get K^2-4K+3=0 which gives K values as 3, 1
For K=3, we get (A-KI)*v=|(2-3) 1| |x|=0 thus we x-y=0 Thus, x=y
|1 (2-3)| |y|
Hence, an accepted value of Eigen vector is |1|. Here we see we can get a lot of Eigen vectors
Normalized Eigen vector, which will be unique for each Eigen value is 1/sqrt(2)|1|
Similarly, the other Eigen vector is 1/sqrt(2) |-1|
| 1|

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Postby pradeeppdy » Fri Apr 04, 2014 6:58 am

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