I do not understand how if det(A) comes out to be a complex number then the eigenvalues will still be real?
2026-03-27 12:03:52.1774613032
Eigenvalues of A(adj A). Are they necessarily real?
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I think you are confusing adjugate from adjoint of a matrix. In this context, it refers to the conjugate transpose.
Guide:
A possible way to solve the problem is to consider the SVD of $A$, compute $A^*$ and then compute $AA^*$ and $A^*A$.