If you take the outer product of two orthogonal 4-dimensional vectors you get a 4*4 matrix. I wonder what you generally can say about this matrix eigenvectors? For example: If 2,3 or 4 of the eigenvalues are zero is it always true that the matrix have at least 2 linear dependent eigenvectors? Maybe this is true regardless of the values of the eigenvalues?(adsbygoogle = window.adsbygoogle || []).push({});

The physical problem is about the operator |a><b| where |a> and |b> are orthogonal to each other and the characteristic polynom is x^4. I have the values for this operator in a basis and it can not be diagonalized.

Is this maybe a general property when |a> and |b> are orthogonal? Or when a couple of the eigenvalues are zero?

If so what is the physics behind this?

Any ideas?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear algebra of operators

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**