Why is the matrix $L_{1}$ norm of this inverse matrix bounded by $rho^{-1}p$?
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Let $Sigma_{n}$ be the sample covariance of size $ptimes p$, and define $Sigma_{n, rho}=Sigma_{n}+rho I$ with $rho>0$, then the matrix $L_{1}$ norm
$$| Sigma_{n,p}^{-1}|_{1}le rho^{-1}p$$.
Could anyone help me to figure out this? It seems very simple, but I have no idea. Thank you!
probability statistics machine-learning
asked Nov 14 at 21:11
dzwang
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up vote
0
down vote
favorite
Let $Sigma_{n}$ be the sample covariance of size $ptimes p$, and define $Sigma_{n, rho}=Sigma_{n}+rho I$ with $rho>0$, then the matrix $L_{1}$ norm
$$| Sigma_{n,p}^{-1}|_{1}le rho^{-1}p$$.
Could anyone help me to figure out this? It seems very simple, but I have no idea. Thank you!
probability statistics machine-learning
asked Nov 14 at 21:11
dzwang
11
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $Sigma_{n}$ be the sample covariance of size $ptimes p$, and define $Sigma_{n, rho}=Sigma_{n}+rho I$ with $rho>0$, then the matrix $L_{1}$ norm
$$| Sigma_{n,p}^{-1}|_{1}le rho^{-1}p$$.
Could anyone help me to figure out this? It seems very simple, but I have no idea. Thank you!
probability statistics machine-learning
asked Nov 14 at 21:11
dzwang
11
Let $Sigma_{n}$ be the sample covariance of size $ptimes p$, and define $Sigma_{n, rho}=Sigma_{n}+rho I$ with $rho>0$, then the matrix $L_{1}$ norm
$$| Sigma_{n,p}^{-1}|_{1}le rho^{-1}p$$.
Could anyone help me to figure out this? It seems very simple, but I have no idea. Thank you!
probability statistics machine-learning
probability statistics machine-learning
asked Nov 14 at 21:11
dzwang
11
asked Nov 14 at 21:11
dzwang
11
asked Nov 14 at 21:11
dzwang
11
asked Nov 14 at 21:11
dzwang
11
asked Nov 14 at 21:11
dzwang
11
11
add a comment |
add a comment |
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