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一道关于半正定的题
Let A and B be semi-definite matrix of the same order, if , then .
已知是同阶半正定,, 则 .
solution: is positive semidefinite, then and are also positive semidefinite.
Because of ,hence all eigenvalues of , are , this is, . Using binomial theorem have .解答: 因为是半正交的,所以,也是半正定的,根据,得到,的特征值全为0,所以, 从而
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