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Results tagged with matrices
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user 113506
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.
6
votes
Accepted
Generalized Cauchy-Binet sum over a fixed subset of indices
This is probably a bit late, but the following formula is proved in this paper (Eq. S4 in the Supplementary Material):
\begin{equation}
\sum_{S \in \binom{[n - j]}{m - j}} \det(A_{[m], S \cup T}) \de …
- 651
3
votes
Accepted
A conjecture about the submatrix of orthogonal matrix
Neither conjecture is true in general, as seen from the following counterexample for $n = 4$, $k = 2$, and
\begin{align}
U = \begin{pmatrix}
0 & 1 & 0 & 0 \\
1 & 0 & 0 & 0 \\
0 & 0 & \frac{1}{\sqrt{2 …
- 651