A是一个矩阵，A^3怎么求 矩阵A的n次方怎么求呢
A\u662f\u4e00\u4e2a\u77e9\u9635\uff0cA^3\u600e\u4e48\u6c42\u56e0\u4e3a|A|\u662f\u4e2a\u6570,A^(-1)\u662f\u4e2a3\u9636\u65b9\u9635,\u6240\u4ee5|A|A^(-1)\u662f\u7528\u6570|A|\u4e58\u4ee53\u9636\u65b9\u9635
A^(-1)\u7684\u6bcf\u4e00\u9879,\u518d\u6c42\u5176\u884c\u5217\u5f0f\u65f6,\u6839\u636e\u884c\u5217\u5f0f\u7684\u6027\u8d28,\u6bcf\u4e00\u884c\uff08\u5217\uff09\u90fd\u53ef\u4ee5\u63d0\u51fa\u6765\u4e00\u4e2a|A|,\u4ece\u800c|A*|=|A|^3*|A^(-1)|.
\u4e00\u822c\u6709\u4ee5\u4e0b\u51e0\u79cd\u65b9\u6cd5\uff1a
1\u3001\u8ba1\u7b97A^2\uff0cA^3 \u627e\u89c4\u5f8b\uff0c\u7136\u540e\u7528\u5f52\u7eb3\u6cd5\u8bc1\u660e\u3002
2\u3001\u82e5r(A)=1\uff0c\u5219A=\u03b1\u03b2^T\uff0cA^n=(\u03b2^T\u03b1)^(n-1)A
\u6ce8:\u03b2^T\u03b1 =\u03b1^T\u03b2 = tr(\u03b1\u03b2^T)
3\u3001\u5206\u62c6\u6cd5\uff1aA=B+C\uff0cBC=CB\uff0c\u7528\u4e8c\u9879\u5f0f\u516c\u5f0f\u5c55\u5f00\u3002
\u9002\u7528\u4e8e B^n \u6613\u8ba1\u7b97\uff0cC\u7684\u4f4e\u6b21\u5e42\u4e3a\u96f6\uff1aC^2 \u6216 C^3 = 0
4\u3001\u7528\u5bf9\u89d2\u5316 A=P^-1diagP
A^n = P^-1diag^nP
\u6269\u5c55\u8d44\u6599\uff1a
\u5c06\u4e00\u4e2a\u77e9\u9635\u5206\u89e3\u4e3a\u6bd4\u8f83\u7b80\u5355\u7684\u6216\u5177\u6709\u67d0\u79cd\u7279\u6027\u7684\u82e5\u5e72\u77e9\u9635\u7684\u548c\u6216\u4e58\u79ef\uff0c\u77e9\u9635\u7684\u5206\u89e3\u6cd5\u4e00\u822c\u6709\u4e09\u89d2\u5206\u89e3\u3001\u8c31\u5206\u89e3\u3001\u5947\u5f02\u503c\u5206\u89e3\u3001\u6ee1\u79e9\u5206\u89e3\u7b49\u3002
\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\uff0c\u76f8\u4f3c\u77e9\u9635\u662f\u6307\u5b58\u5728\u76f8\u4f3c\u5173\u7cfb\u7684\u77e9\u9635\u3002\u76f8\u4f3c\u5173\u7cfb\u662f\u4e24\u4e2a\u77e9\u9635\u4e4b\u95f4\u7684\u4e00\u79cd\u7b49\u4ef7\u5173\u7cfb\u3002\u4e24\u4e2an\u00d7n\u77e9\u9635A\u4e0eB\u4e3a\u76f8\u4f3c\u77e9\u9635\u5f53\u4e14\u4ec5\u5f53\u5b58\u5728\u4e00\u4e2an\u00d7n\u7684\u53ef\u9006\u77e9\u9635P\u3002
\u4e00\u4e2a\u77e9\u9635A\u7684\u5217\u79e9\u662fA\u7684\u7ebf\u6027\u72ec\u7acb\u7684\u7eb5\u5217\u7684\u6781\u5927\u6570\u76ee\u3002\u7c7b\u4f3c\u5730\uff0c\u884c\u79e9\u662fA\u7684\u7ebf\u6027\u65e0\u5173\u7684\u6a2a\u884c\u7684\u6781\u5927\u6570\u76ee\u3002\u901a\u4fd7\u4e00\u70b9\u8bf4\uff0c\u5982\u679c\u628a\u77e9\u9635\u770b\u6210\u4e00\u4e2a\u4e2a\u884c\u5411\u91cf\u6216\u8005\u5217\u5411\u91cf\uff0c\u79e9\u5c31\u662f\u8fd9\u4e9b\u884c\u5411\u91cf\u6216\u8005\u5217\u5411\u91cf\u7684\u79e9\uff0c\u4e5f\u5c31\u662f\u6781\u5927\u65e0\u5173\u7ec4\u4e2d\u6240\u542b\u5411\u91cf\u7684\u4e2a\u6570\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u77e9\u9635
直接按定义, A^3 = A*A*A
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