Rayleigh-Ritz Theorem

S_David

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