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The most popular device used for a solution of plenty of DSP problems is CORDIC processor for orthogonal transformation of a plane rotation by Volder's algorithm. This algorithm have been employed in a number of special purpose processor arrays due to efficient realization of various types of linear transformations using simple hardware components. The dimensionality of CORDIC-algorithms is equal to two. This is the major disadvantage. A long sequence of these macro-operations is required for practical problem solving. Taking into account that very fast growth of modern VLSI technology offers a hardware realization of an ever-growing share of mathematical means it seems reasonable to speed up matrix computations by expressing them in terms of higher dimensional transformations. The present book is a short survey of research results which were published by author in this area for resent years.