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Activity Number:
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256
- Contributed Poster Presentations: Section on Statistical Learning and Data Science
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Type:
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Contributed
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Date/Time:
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Monday, July 29, 2019 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Learning and Data Science
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Abstract #304335
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Title:
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Big, Bad Matrices: a Constructive Approach
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Author(s):
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Garrett Mulcahy* and Thomas Sinclair
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Companies:
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Purdue University and Purdue University
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Keywords:
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random matrices ;
asymptotics;
data science
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Abstract:
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John von Neumann's "Approximative Properties of Matrices of High Finite Order"(1941) explores the asymptotic behavior of matrices as dimension increases but remains finite. Essentially, von Neumann ventured to explore the neglected middle ground between finite and infinite dimensional analysis. The major result of this paper is a proof of the existence of "big, bad matrices"— that is, matrices of large dimension that possess "bad" qualities. von Neumann's proof was nonconstructive, making use of what he called a "volumetric" argument. We utilize computational techniques in a quest to find a construction of these matrices; discovering what the matrices look like will potentially have applications to data science and the theory of random matrices.
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Authors who are presenting talks have a * after their name.
