Bad Qubits — Learn Quantum by Doing

Multiple choice

According to the spectral theorem for a Hermitian operator A on a finite-dimensional complex Hilbert space, which statement is guaranteed to be true?

All eigenvalues of A are real, and there exists an orthonormal basis of the whole space made of eigenvectors of A
A has exactly one eigenvalue, which may be any complex number
The eigenvectors of A span only a proper subspace, never the whole space
All eigenvalues of A lie on the unit circle, and A is its own inverse