- #1

shankar

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can anyone explain the the real meaning and purpose of eigen vlaue and eigen vectors..

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- Thread starter shankar
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- #1

shankar

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can anyone explain the the real meaning and purpose of eigen vlaue and eigen vectors..

- #2

Hurkyl

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Consider the fact that (nearly) every square matrix can, after a suitable change of basis, be written as a diagonal matrix whose entries are simply its eigenvalues.

So in one sense, using eigenvalues and eigenvectors let's you treat (nearly) any matrix similarly to a diagonal matrix, making the work easier.

- #3

Lonewolf

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- #4

HallsofIvy

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Essentially, the eigenvectors are those vectors on which the linear tranformation acts like simple scalar multiplication.

- #5

Oxymoron

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Q) So if you have some vector then scalar multiples of it only 'stretches' or 'compresses' it by a factor of your eigenvalue? Explain. And how can we use determinants in finding eigenvalues of a given matrix?

(off-topic) Has this got anything to do with the Kronecker Delta in Tensor Calculus?

- #6

quantumdude

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Originally posted by Oxymoron

(off-topic) Has this got anything to do with the Kronecker Delta in Tensor Calculus?

Yes, it does.

When calculating the eigenvalues {λ

det(A-λI)=0.

If we rewrite that in terms of matrix elements (IOW, with indices) we can write:

det(A

the identity matrix I

- #7

shankar

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finding eigen vector for the matrix A, will it give the orthogonal quantity of the matrix..

- #8

mathwonk

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see http://www.math.uga.edu/~roy/

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