Let $T_1, \ldots, T_n$ by real symmetric positive definite matrices, with eigenvalues bounded below by $\mu > 0$. Can I say $$ \frac{x^T T_1 T_2 \ldots T_n x}{x^T x} \geq \mu^n $$ I know you can say this for a product of two matrices (e.g., Eigenvalues of the product of two symmetric matrices), but what about the case where I have $n \geq 2$ matrices in the product? If these matrices commute the result is straightforward, but I'm interested in the case where these matrices don't necessarily commute.
Eigenvalues of product of symmetric positive definite matrices
Mido
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