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nhigham.com | ||
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nickhar.wordpress.com
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| | | | | 1. Low-rank approximation of matrices Let $latex {A}&fg=000000$ be an arbitrary $latex {n \times m}&fg=000000$ matrix. We assume $latex {n \leq m}&fg=000000$. We consider the problem of approximating $latex {A}&fg=000000$ by a low-rank matrix. For example, we could seek to find a rank $latex {s}&fg=000000$ matrix $latex {B}&fg=000000$ minimizing $latex { \lVert A - B... | |
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francisbach.com
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djalil.chafai.net
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| | | | | This post is devoted to few convex and compact sets of matrices that I like. The set \( {\mathcal{C}_n} \) of correlation matrices. A real \( {n\times n} \) matrix \( {C} \) is a correlation matrix when \( {C} \) is symmetric, semidefinite positive, with unit diagonal. This means that \[ C_{ii}=1, \quad C_{ji}=C_{ji},\quad \left\geq0 \] for every \(... | |
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siddhartha-gadgil.github.io
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| | | [AI summary] The text discusses a formalization in Lean 4 of a mathematical result related to the group P and the unit conjecture. It outlines the construction of the group P as a metabelian group with a specific action and cocycle, the proof of its torsion freeness, and the use of decidable equality and enumeration to verify properties. The formalization also includes the construction of the group ring and the verification of Gardam's disproof of the unit conjecture by demonstrating the existence of a non-trivial unit in the group ring over the field F₂. | ||
