Operator Scaling: Theory and Applications

In this paper, we present a deterministic polynomial time algorithm for testing whether a symbolic matrix in non-commuting variables over Q is invertible or not. The analogous question for commuting variables is the celebrated polynomial identity testing (PIT) for symbolic determinants. In contrast...

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Bibliographic Details
Published in:	Foundations of computational mathematics Vol. 20; no. 2; pp. 223 - 290
Main Authors:	Garg, Ankit, Gurvits, Leonid, Oliveira, Rafael, Wigderson, Avi
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.04.2020 Springer Nature B.V
Subjects:	Algorithms Applications of Mathematics Approximation Commuting Complexity Computer Science Economics Information theory Linear algebra Linear and Multilinear Algebras Lower bounds Math Applications in Computer Science Mathematics Mathematics and Statistics Matrices (mathematics) Matrix Theory Numerical Analysis Operators (mathematics) Optimization Polynomials Quantum computing Quantum phenomena Questions System theory Systems theory Non-commutative algebra 68Q25 Quantum operators Polynomial identity testing Invariant theory Derandomization 68Q10
ISSN:	1615-3375, 1615-3383
Online Access:	Get full text
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