We study the prime decomposition of a quadratic monic matrix polynomial. From the prime decomposition of a quadratic matrix polynomial, we obtain a formula of the general solution to the corresponding second-order differential equation. For a quadratic matrix polynomial with pairwise commuting coefficients, we get a sufficient condition for the existence of a prime decomposition.
Citation: Yunbo Tian, Sheng Chen. Prime decomposition of quadratic matrix polynomials[J]. AIMS Mathematics, 2021, 6(9): 9911-9918. doi: 10.3934/math.2021576
We study the prime decomposition of a quadratic monic matrix polynomial. From the prime decomposition of a quadratic matrix polynomial, we obtain a formula of the general solution to the corresponding second-order differential equation. For a quadratic matrix polynomial with pairwise commuting coefficients, we get a sufficient condition for the existence of a prime decomposition.
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Yunbo Tian, Sheng Chen. Prime decomposition of quadratic matrix polynomials[J]. AIMS Mathematics, 2021, 6(9): 9911-9918. doi: 10.3934/math.2021576
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