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Results tagged with matrices
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user 479369
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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Maximal eigenvalue of a correlation matrix with some entries fixed as zeros
The question can be solved by considering the Lovász number of a graph whose adjacency matrix has entries $0$ if $a_{ij} \neq 0$ and $1$ everywhere else. This is proven (up to a typo) in Section 33 he …
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Maximal eigenvalue of a correlation matrix with some entries fixed as zeros
Those matrices are sometimes referred to as correlation matrices. From the positivity of the minors, we know that each matrix element $a_{ij}$ satisfies $-1 \leq a_{ij} \leq 1$. … Note that the only PSD $\{0,1\}$-matrices are block-diagonal matrices with blocks consisting of only ones (up to some permutation). …
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