Positive square root of an operator
= Positive square root of an operator
{title2=$T^{1/2}$}
Every bounded <positive operator> $T$ has a unique positive operator $T^{1/2}$ satisfying $(T^{1/2})^2=T$. The <spectral theorem for normal operators on a separable Hilbert space> constructs it by applying the scalar square-root function to the spectrum.