On Quantum Tangential Spacetime as a finite Hilbert-Space

Nature knows no zero. On a fundamental level there is a minimal length. If there has to be a sort of quantum-spacetime it can not include fourvectors but must be described in tensor-form from first principles. Every coordinate, even in tangential spacetime without gravity-force has constant components in other dimensional directions, which can‘t be set to zero but must be defined over Planck-lenghts. In this case tangential spacetime has to be rewritten in a corrected form. This rewriting will be done. Maybe, from this calculation there can later derived a consistent version of quantum gravity, which leads to finite physical states in this theory. In , there is ergo constructed a Frobenius-scalarproduct of matrices and therefore a finite Hilbert-space. A Hilbert space is a real or complex vector space with a dot product , which is complete with respect to the norm induced by the dot product, i.e. in which every Cauchy sequence converges. A Hilbert space is therefore a complete pre-Hilbert space. Therefore the matrix space K (m × n) of the real or complex matrices with the Frobenius -scalar product is a Hilbertspace.