Group-Pattern Matrices - Roger Chalkley
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Résumé : This mathematical monograph uses the concept of a group-pattern throughout to conveniently characterize various matrices of unusual historical interest. No prior knowledge about groups is needed. A group-pattern for a group G having n elements is provided by the n x n interior of any multiplication table for G in which the identity element of G occupies each of the n principal diagonal positions. A group-pattern matrix results when each group element in the group-pattern is replaced at each of its positions by an element of a given set. For the key specializations of this definition, complete details and new viewpoints are presented.
Biographie:
Roger Chalkley earned the degree of Ch.E. in 1954 at the University of Cincinnati where he earned an A.M. (mathematics) in 1956 and a Ph.D. (mathematics) in 1958. Since 1989, his research has focused on invariants for ordinary differential equations. To revive that truly interesting subject, it is advantageous to regard invariants as differential polynomials into which substitutions can be made. Then, as elements of a differential ring, they can be constructed in terms of simpler members....