  The bra-ket formalism is generally applied to carry out representation-free
considerations in quantum mechanics. It provides efficient means for this
purpose, but at the same time, drawbacks are inherent in it. Some of these
originate from the fact that the bra-ket notation is not suitable to handle the
domains of the definitions of operators involved. An additional drawback is
that the bra-ket formalism, being a dual-space formalism, excludes the natural
one-space point of view.
  In the present work, a concise representation-free scheme is constructed.
This scheme has no drawbacks of the bra-ket formalism. At the same time, this
scheme provides the efficient means to carry out quantum mechanical
considerations, such as all those offered by the bra-ket scheme. The present
scheme allows both the one-space and dual-space interpretations, in contrast to
the bra-ket scheme.
  Before the above, the strengths and drawbacks of the bra-ket formalism are
addressed.
