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SPRING 2015 Apolarity for determinants and permanents of generic matrices
Sepideh Masoumeh Shafiei
J. Commut. Algebra 7(1): 89-123 (SPRING 2015). DOI: 10.1216/JCA-2015-7-1-89

Abstract

We show that the apolar ideals to the determinant and permanent of a generic matrix, the Pfaffian of a generic skew symmetric matrix and the hafnian of a generic symmetric matrix are each generated in degree~2. As a consequence, using a result of Ranestad and Schreyer, we give lower bounds to the cactus rank and rank of each of these invariants. We compare these bounds with those obtained by Landsberg and Teitler.

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Sepideh Masoumeh Shafiei. "Apolarity for determinants and permanents of generic matrices." J. Commut. Algebra 7 (1) 89 - 123, SPRING 2015. https://doi.org/10.1216/JCA-2015-7-1-89

Information

Published: SPRING 2015
First available in Project Euclid: 2 March 2015

zbMATH: 1364.13024
MathSciNet: MR3316987
Digital Object Identifier: 10.1216/JCA-2015-7-1-89

Subjects:
Primary: 13H10, 14N15

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.7 • No. 1 • SPRING 2015
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