quantum mechanics - What is an antiunitary operator?

What is an antiunitary operator? In field theory one can define a time reversal operator $T$ such that $T^{-1} \phi (x) T = \phi (\mathcal T x)$. It is then proved that $T$ must be antiunitary: $T^{-1} i T = -i$.

How is this equation to be understood? If $i$ is just the unit complex number, why don't we have $T^{-1} i T = i T^{-1} T$ which is just the identity times $i$?

Answer

If I correctly understood your misunderstanding, the answer is: operator is not always a matrix. Technically, action of time inversion operator contains complex conjugation. E.g., in spin up/spin down basis it is written as $-i\sigma_y\mathcal{K}$, where $\mathcal{K}$ is complex conjugation.