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Results tagged with matrices
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user 151366
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
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Eigenvalues of product of symmetric positive definite matrices
Let $T_1, \ldots, T_n$ by real symmetric positive definite matrices, with eigenvalues bounded below by $\mu > 0$. … Can I say
$$
\frac{x^T T_1 T_2 \ldots T_n x}{x^T x} \geq \mu^n
$$
If these matrices commute the result is straightforward, but I'm interested in the case where these matrices don't necessarily commute. …
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