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Nik Weaver
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Existence of double eigenvalue

Let $A$ and $B$ be complex $4\times 4$ matrices. Assume both are Hermitian, and that they are linearly independent.

Must there exist a nonzero real linear combination $aA + bB$ which has a repeated eigenvalue?

Nik Weaver
  • 42.8k
  • 3
  • 112
  • 213