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Results tagged with matrices
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user 110824
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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Submodularity property of trace of inverse matrix
I.e., does given any real symmetric positive-definite matrices $X,A,B$
$$
\tr X^{-1} + \tr(X+A+B)^{-1} \geq \tr(X+A)^{-1} + \tr(X+B)^{-1}
$$
hold? … UPD: I have checked it numerically, it appears that it does not hold for the following matrices:
\begin{equation}
\begin{split}
X &= \begin{pmatrix} 0.08151549 & 0.05234424\\ 0.05234424 & 0.17050588 \end …
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