Question

For each eigen value of the matrix A(3x3), the number of eigen vectors=____ @IIT study group

Answer 1

"While an matrix always has eigenvalues, some or all of which may be degenerate, such a matrix may have between 0 and linearly independent eigenvectors" - wolframalpha.com

Answer 2

While an nxn matrix ..... between 0 and n linearly independant eigenvectors

Answer 3

but that doesnt answer the "for each value" ...

Answer 4

IIT JEE preparation huh ?

Answer 5

Oh cool .. I would probably try for it someday ...

Answer 6

I wish i understood these better, but I think this might be it:

"Thus, for every eigenvalue ci this equation constitutes a system of n simultaneous homogeneous equations, and every system of equations has an infinite number of solutions. Corresponding to every eigenvalue ci is a set of eigenvectors Xi, the number of eigenvectors in the set being infinite."

http://www.miislita.com/information-retrieval-tutorial/matrix-tutorial-3-eigenvalues-eigenvectors.html#eigenvectors

Answer 7

Any idea with regards to your material?

Answer 8

As far as I can tell, if we restrict the vectors to unit lengths, then there should only be 2 Evectors for each Evalue, a left and a right. But none of this is definitive since I myself just started to learn these

Answer 9

I have the key as infinite... So i think what u said first is correct... As I havent understood the reason, I have posted the question...Thank you@amistre64... Thanks for the link also... :)

Answer 10

if v is an eigenvector for lambda then so is a*v for any non zero constant a.