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The polynomial representations for the matrix pair with the sum and product being equal without any constrained conditions

Xiaoxia Feng, Zhongpeng Yang, Hongbin LV, Meixiang Chen, Chenyu Xu

Abstract


We point out the minimal polynomials of the matrix pair with the sum and product being equal are mutually determined, furthermore, we prove there exists the unique polynomial pair such that the matrix pair with the sum and product being equal represent each other, simultaneously, we obtain the computational formulas of those polynomial pairs. Moreover, we generalize and improve the corresponding results with the constrained conditions, and show that the polynomial representations for the matrix pair with the sum and product being equal are without constrained conditions.

Keywords


matrix pair with the sum and product being equal; minimal polynomial; polynomial representation; degree of polynomial.

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