  In quantum mechanics (formulated, say, in Schr\"{o}dinger picture) only the
knowledge of a complete set of observables $\Lambda_j$ enables us to declare
the related physical inner product (i.e., the Hilbert-space metric $\Theta$
such that $\Lambda_j^\dagger \Theta=\Theta\,\Lambda_j$, i.e., such that
$\Theta=\Theta(\Lambda_j)$) unique. In many applications people simplify the
model and consider just a single input observable (mostly an
energy-representing Hamiltonian $\Lambda_1=H$) and pick up, out of all of the
eligible metrics $\Theta=\Theta(H)$, just the simplest candidate (typically, in
the case of the special self-adjoint input $H$ we virtually always work with
trivial $\Theta=I$). As long as this forces us to admit only the self-adjoint
forms of any other input observable $\Lambda_j$, the scope of the theory is,
without any truly meaningful phenomenological reason, restricted. In our
present paper we describe a strictly non-numerical $N$ by $N$ matrix model in
which such a restriction is replaced by another, phenomenologically
non-equivalent restriction in which $\Theta \neq I$ and in which the system
reaches a collapse (i.e., a loss-of-bservability catastrophe) via unitary
evolution.
