Invariants and canonical forms for linear multivariable systems under the action of orthogonal transformation groups

Subject of the present paper is the study and construction of complete independent invariants and canonical forms for linear multivariable systems under the action of orthogonal transformation groups. Stable computational algorithms for finding the orthogonal canonical forms are presented and their numerical properties are discussed. In view of their nice numerical properties the orthogonal canonical forms are preferable for computations. They reveal the basic invariant structure of linear multivariable systems and provide the same theoretical advantages as the canonical forms relative to general transformation groups.

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