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The main aim of this paper is the presentation of the connection between the elements of the classical matrix arithmetic in case of three-by-three arbitrary real matrices. The given formulae can be used as well in case of the topic of stability analysis connected to the characteristic polynomial. The theorems and formulae presented in this article can be used in linear algebra courses or e.g. in three Degrees-of-Freedom mechanical problems, in machine tool bases designing, or in analyzes of earthquake effect on different type of structures.

Alternative Method to Determine the Characteristic Polynomial Applying Three-by-Three Matrices