由 $A$ 半正定知存在矩阵 $B$ 使得 $$eex ea A=B^tB& a 0=a_{ii}=sum_j b_{ji}^2\ & a b_{ji}=0, forall j\ & a seddm{ a_{il}=sum_j b_{ji}b_{jl}=0\ a_{ki}=sum_j b_{jk}b_{ji}=0 }. eea eeex$$
由 $A$ 半正定知存在矩阵 $B$ 使得 $$eex ea A=B^tB& a 0=a_{ii}=sum_j b_{ji}^2\ & a b_{ji}=0, forall j\ & a seddm{ a_{il}=sum_j b_{ji}b_{jl}=0\ a_{ki}=sum_j b_{jk}b_{ji}=0 }. eea eeex$$