Is the log norm square of a holomorphic function plurisubharmonic?

Question

For a reminder a differentiable function $f:\mathbb{C}^n\rightarrow \mathbb{C}$ is plurisubharmonic iff the matrix $$\frac{\partial^2 f}{\partial z_i\partial\bar{z}_j}$$ is positive semi-definite (wikipedia).

Now let $f:\mathbb{C}^n\rightarrow \mathbb{C}$ be a holomorphic function. Is the function $\log ||f||^2$ plurisubharmonic ?