230问答网 > 为什么正交矩阵能使矩阵化为对角阵

为什么正交矩阵能使矩阵化为对角阵

2025-03-19 04:28:17
推荐回答（3个）
回答1：

P^-1AP = 对角矩阵
正交对角化要求 P 是正交矩阵,即P可逆且 P^-1 = P^T
即是相似变换又是合同变换,用于二次型
可逆矩阵相似对角化
一般考虑的是方阵,并不要求方阵可逆,要求 P 可逆
可对角化就是A可相似对角化,即存在可逆矩阵P使得 P^-1AP = 对角矩阵

回答2：

找本教材，把奇异值分解看一遍

回答3：

对角相等

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