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## Homework Statement

Hi all.

Let's say that I have a Hermitian 2x2 matrix

**A**with two distinct eigenvalues, and thus two eigenvectors.

**Question 1:**What space is it they span? Is it

**R**

^{2}?

Now let us say I have another Hermitian 2x2 matrix

**B**with two distinct eigenvalues, and thus two eigenvectors.

**Question 2:**Do the eigenvectors of

**B**span the same space as the eigenvectors of

**A**?

Thanks in advance.

Sincerely,

Niles.