how to solve eigen values and vectors without the expression eig

how to write a matlab code to generate eigen values and vectors of the matrix A=[1,1;4,-2] the code should not involve [x,y]=eig(A) ,, it should be another way

[Christine Tobler]

Why don't you want to use EIG? Is this for an exercise, or is the function not available for some reason?

[Patrick Franks]

In my case, EIG doesn't behave correctly for matrices that are 5x5 or larger when compiled into C on a target computer. The eigenvalues can still be calculated by finding the roots of the characteristic polynomial of the matrix [i.e. roots(poly(A))], but eigenvectors also need to be calculated without using eig.

Using the null space of A-lamda*I has been suggested, but for some reason the matrix A-lamda*I in my case is not rank-deficient.

Answer 1

[Matt J]

Potentially useful commands: ROOTS, POLY, NULL

[Sunil Patil]

HI,

I have used 'null' function to find the eigen vectors null(A-lamda*I).

obtained eigen vectors are not matching with the vactors getting by eig() function.

does it need vector normalisation ?

Kindly suggest..

Thanks

Sunil Patil

[Matt J]

There might be differences in sign. Or, the null space of A-lamda*I might be multi-dimensional, If so, null() and eig() may not return the same basis for that space.