Polinomul caracteristic al unei matrice in raport cu alta matrice
The characteristic polynom of a matrix in relation to another matrix

Summary/Abstract: The following work considers that the characteristic polynomial of a square matrix of order n is defined in relation to the square matrix In, this observation allows us to expand the notion of the characteristic polynomial of a matrix A in relation to another square matrix of the same order with A, the polynomial coefficients being sums of mixed determinants. This polynomial allows for a generalization of the Cayley-Hamilton relation for two matrixes A and B that commute and afterwards form the necessary and adequate conditions for the forming of two homogenous and invertible matrixes of grade p of the two matrixes A and B. Interesting to note is also an intermediary result, the lemma of the two polynomial matrixes, that can lead to the generating of new mathematical identities.

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