  The Dirac's bra-ket formalism is generalized to finite-dimensional vector
spaces with indefinite metric in a simple mathematical context similar to
thatof the theory of general tensors where, in addition, scalar products are
introduced with the help of a metric operator. The specific calculation rules
are given in a suitable intuitive notation. It is shown that the proposed
bra-ket calculus is appropriate for the general theory of basis transformations
and finite-dimensional representations of the symmetry groups of the metric
operators. The presented application is the theory of finite-dimensional
representations of the $SL(2,\Comp)$ group with invariant scalar products.
Pacs: 02.10.Sp, 02.20.Qs
