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Abstract
An algorithm is developed to solve a special case of reverse problems of linear systems, and as its application, a method is presented to solve optimal problem over the special orthogonal group. An algorithm is designed to find out an orthogonal matrix A such that A transforms a set of orthogonal vectors to another, and as its application, a method is given to generate subgroups of the orthogonal group preserving several orthogonal vectors fixed. It is prove that the symmetric (or rotational) group of the simplex S n preserving its center fixed is isomorphic to the group consisting of all n × n permutational matrices. All algorithms in this paper can be realized by algebraic system CoCoA 4.3.
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