I'm working on some math that falls out of using a Kalman filter for estimation. I'd like to show that [tex]|G^T C_1^{-1} G + C_2^{-1}| \leq |G^T [diag(C_1)]^{-1} G + C_2^{-1}|[/tex] where [tex]C_1[/tex] and [tex]C_2[/tex] are covariance matrices and [tex]diag(C_1)[/tex] denotes the diagonal of matrix A.(adsbygoogle = window.adsbygoogle || []).push({});

I've been able to show this is true when [tex]G=G^T=I[/tex] and [tex]C_2[/tex] is also diagonal. Numerical simulations suggest it is more generally true but I've been unable to convince myself of it on paper.

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# Obscure determinant question

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