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Homework Statement
Given matrix A:
a 1 1 ... 1
1 a 1 ... 1
1 1 a ... 1
.. . .. ... 1
1 1 1 ... a
Show there is an eigenvalue of A whose geometric multiplicity is n-1. Express its value in terms of a.
Homework Equations
general eigenvalue/vector equations
The Attempt at a Solution
My problem is I'm not sure how to start it off.
I can state A is square, symmetric and hermitian so I know it has to do with one or more of those. I tried going through using a determinant but it didn't seem to work nicely, I have a feeling that it might have to do with a property of symmetric matrices but am not sure how to go about the proof (or which property)