= Unitary equivalence
{title2=$B=UAU^{-1}$}
= Unitarily equivalent
{synonym}
Two operators on <Hilbert spaces> are unitarily equivalent if a <unitary operator> maps their operator domains onto one another and intertwines their actions. Their <spectra> and <eigenvalue> multiplicities then agree. For nonnegative <self-adjoint operators> it suffices that the unitary maps their closed <quadratic form> domains onto one another and preserves the forms, since the associated operator is determined by the form.
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