Abstract: Consider a weighted undirected graph and its corresponding Laplacian matrix, possibly augmented with additional diagonal elements corresponding to self-loops. The Kron reduction of this ...
This course provides an introduction to linear algebra topics. Emphasis is placed on the development of abstract concepts and applications for vectors, systems of equations, matrices, determinants, ...
This post continues the series from the Adjoint School of Applied Category Theory 2022. It is a summary of the main ideas introduced in this paper: Filippo Bonchi, Dusko Pavlovic and Pawel Sobocinski, ...
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Abstract: We give a self-contained proof of a recently established $\mathcal{B}\left( \mathcal{H} \right)$-valued version of Jaffards Lemma. That is, we show that the Jaffard algebra of ...
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ABSTRACT: An in-depth description of an apparently forgotten matrix operation, the reversal operator, is developed. The properties of such an operation are also given, resulting in a new vector-matrix ...
In the past few decades, multi-linear algebra also known as tensor algebra has been adapted and employed as a tool for various engineering applications. Recent developments in tensor algebra have ...
Introduction: Compared to Genome-Wide Association Studies (GWAS) for common variants, single-marker association analysis for rare variants is underpowered. Set-based association analyses for rare ...
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