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wall_2012

铁虫 (小有名气)

[求助] 矩阵正定性判定

假设矩阵为非列满秩矩阵,,记
如何判定为正定矩阵???
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hank612

至尊木虫 (著名写手)

你的Px中间那部分是广义逆么?
http://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse

如果是的话, 楼主要先说明这个形式的广义逆是非负定的(就是矩阵M 满足)

那么, 对于任意向量u, 令v=X'G'u, 有(G(Px+XX')G'u,u)=(((XX')^-+Im)v,v) >= (v,v).
然后说明 v不等于零  就万事大吉了.
We_must_know. We_will_know.
2楼2015-03-18 01:53:06
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