Hi! I am a new user who is not an expert with Linear Algebra at all.(adsbygoogle = window.adsbygoogle || []).push({});

I have some questions about eigen values/vectors and their meaning with relation to a 2x2 matrix, or tensor, which was obtained by the tensor product of 2 vectors.

First, I have two 2-dimensional 2x1 vectors "v1" and "v2" on one point from which I wish to construct a 2x2 matrix "T" using tensor product, ie T=v1 (circle x) v2.

Then, I compute the eigen values and eigen vectors of the matrix (tensor) T.

Questions:

Is using tensor product the correct way to represent the vectors v1 and v2 on a 2x2 matrix T?

What's the meaning of the eigen values and eigen vectors of T? What is their relation with the original vectos v1 and v2? Also, most importantly, what is the meaning of having eigen values that are repeated?

I have read that if the eigen values of T are repeated, then that means that any eigen vector is associated with T, but still cannot figure out its underlying meaning with respect to the original vectors that constructed T.

Thanks!

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# Meaning of eigenvectors and values of a 2x2 matrix (2nd order tensor)

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