类比关于数式的二项式定理，导出关于矩阵的二项式定理，并用数学归纳法予以证明，最后举例说明关于矩阵的二项式定理的应用。
Compared to digital binomial function, matrix binomial function is derived and proved with induction method and the application of it is illustrated with examples.
本文按照这种算法总结出完成四柱汉诺塔游戏之最少步数的公式，并用数学归纳法证明了它。
According to that algorithm, this article puts forward a formula to calculate the number of movements necessary for the 4-peg Hanoi Tower problem, and proves it using mathematical induction.
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