It is theoretically important to solve the problems of decomposition of automorphisms of solvable subalgebra and nilpotent subalgebra of matrix algebra over commutative rings.
交换环上矩阵代数的可解子代数和幂零子代数的自同构分解问题是一类重要的具有理论意义的研究课题。
Both methods can be solved explicitly by a pseudo-inverse matrix and are of invertible, commutative, and associative properties, which enhance the efficiency and controllability of the manipulation.
两种方法都可以利用广义逆矩阵求得显式解，具有可逆性、可交换性、结合性等优点，提高了曲面形状修改的效率和可控性。
Both methods can be solved explicitly by a pseudo-inverse matrix and are of invertible, commutative, and associative properties, which enhance the efficiency and controllability of the manipulation.
两种方法都可以利用广义逆矩阵求得显式解，具有可逆性、可交换性、结合性等优点，提高了曲面形状修改的效率和可控性。
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