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Rayleigh-Ritz Theorem

by S_David
Tags: rayleighritz, theorem
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S_David
#1
Mar14-12, 02:24 AM
P: 597
Hi,

I have the following

[tex]\underset{\|\mathbf{x}\|^2=1}{\text{max }}\mathbf{x}^{H}\mathbf{A}^{-1}\mathbf{x}=\lambda_{\text{max}}\left(\mathbf{A^{-1}}\right)[/tex]

which is the maximum singular value of the inverse of a diagonal matrix A. Now does this equivalent to

[tex]\lambda_{\text{min}}\left(\mathbf{A}\right)[/tex]

which is the minimum singular value of the matrix A?

Thanks
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