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Article

On Lagrangian Grassmannian Variety and Plücker Matrices

by
Jesús Carrillo-Pacheco
Academia de Matemáticas, Universidad Autónoma de la Ciudad de México, Ciudad de México 09390, Mexico
Mathematics 2024, 12(6), 858; https://doi.org/10.3390/math12060858
Submission received: 18 January 2024 / Revised: 3 March 2024 / Accepted: 4 March 2024 / Published: 14 March 2024
(This article belongs to the Special Issue Advances of Linear and Multilinear Algebra)

Abstract

The Plücker matrix BL(n,E) of the Lagrangian Grassmannian L(n,E), is determined by the linear envelope L(n,E) of the Lagrangian Grassmannian. The linear envelope L(n,E) is the intersection of linear relations of Plücker of Lagrangian Grassmannian, defined here. The Plücker matrix BL(n,E) is a direct sum of the incidence matrix of the configuration of subsets. These matrices determine the isotropy index rn and rn-atlas which are invariants associated with the symplectic vector space E.
Keywords: Lagrangian Grassmannian; Linear Envelope; Contraction Map; Incidence Matrices; Radical Ideal; Seindeber’s lemma Lagrangian Grassmannian; Linear Envelope; Contraction Map; Incidence Matrices; Radical Ideal; Seindeber’s lemma

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MDPI and ACS Style

Carrillo-Pacheco, J. On Lagrangian Grassmannian Variety and Plücker Matrices. Mathematics 2024, 12, 858. https://doi.org/10.3390/math12060858

AMA Style

Carrillo-Pacheco J. On Lagrangian Grassmannian Variety and Plücker Matrices. Mathematics. 2024; 12(6):858. https://doi.org/10.3390/math12060858

Chicago/Turabian Style

Carrillo-Pacheco, Jesús. 2024. "On Lagrangian Grassmannian Variety and Plücker Matrices" Mathematics 12, no. 6: 858. https://doi.org/10.3390/math12060858

APA Style

Carrillo-Pacheco, J. (2024). On Lagrangian Grassmannian Variety and Plücker Matrices. Mathematics, 12(6), 858. https://doi.org/10.3390/math12060858

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