In this paper it is shown a possibility of creating efficient computing technology for solving matrix-vector-based scientific, engineering, encomic, and other problems. It is based on using the new class of hypercomplex systems opened by W.F. Hamilton but formed by a procedure which is different from the procedure proposed by his followers. This method allows, for example, to reduce multiplication/summation of two large size matrixes/vectors to multiplication/summation of only two whole numbers and, in general, to use a single real number as an operand instead of matrix/vector. Transforming matrices and vectors into whole numbers can be performed on the basis of parallel massive/multiprocessor systems.
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