Generalized "bra-ket" formalism

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