Complex conference matrices and equi-isoclinic planes in Euclidean spaces

A. Blokhuis; Ulrich Brehm; Boumediene Et-Taoui

doi:10.1007/s13366-017-0374-2

Complex conference matrices and equi-isoclinic planes in Euclidean spaces

A. Blokhuis
, Ulrich Brehm
, Boumediene Et-Taoui (Corresponding author)

Research output: Contribution to journal › Article › Academic › peer-review

7 Citations (Scopus)

Abstract

We demonstrate that if there exists a real symmetric conference matrix of order n, then there exists a complex symmetric conference matrix of order n- 1. A v-set of equi-isoclinic planes in R ⁿ is a set of v planes spanning R ⁿ, each pair of which has the same non-zero angle arccosλ. We prove that for any integer n≥ 5 for which there exists a complex symmetric conference matrix of order n, the maximum number of equi-isoclinic planes with angle arccos 1n-1 in R ⁿ is equal to n.

Original language	English
Pages (from-to)	491-500
Number of pages	10
Journal	Beiträge zur Algebra und Geometrie = Contributions to Algebra and Geometry
Volume	59
Issue number	3
DOIs	https://doi.org/10.1007/s13366-017-0374-2
Publication status	Published - 1 Sept 2018

Keywords

Complex conference matrices
Equi-isoclinic planes

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10.1007/s13366-017-0374-2

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abstract = "We demonstrate that if there exists a real symmetric conference matrix of order n, then there exists a complex symmetric conference matrix of order n- 1. A v-set of equi-isoclinic planes in R n is a set of v planes spanning R n, each pair of which has the same non-zero angle arccosλ. We prove that for any integer n≥ 5 for which there exists a complex symmetric conference matrix of order n, the maximum number of equi-isoclinic planes with angle arccos 1n-1 in R n is equal to n. ",

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T1 - Complex conference matrices and equi-isoclinic planes in Euclidean spaces

AU - Blokhuis, A.

AU - Brehm, Ulrich

AU - Et-Taoui, Boumediene

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Y1 - 2018/9/1

N2 - We demonstrate that if there exists a real symmetric conference matrix of order n, then there exists a complex symmetric conference matrix of order n- 1. A v-set of equi-isoclinic planes in R n is a set of v planes spanning R n, each pair of which has the same non-zero angle arccosλ. We prove that for any integer n≥ 5 for which there exists a complex symmetric conference matrix of order n, the maximum number of equi-isoclinic planes with angle arccos 1n-1 in R n is equal to n.

AB - We demonstrate that if there exists a real symmetric conference matrix of order n, then there exists a complex symmetric conference matrix of order n- 1. A v-set of equi-isoclinic planes in R n is a set of v planes spanning R n, each pair of which has the same non-zero angle arccosλ. We prove that for any integer n≥ 5 for which there exists a complex symmetric conference matrix of order n, the maximum number of equi-isoclinic planes with angle arccos 1n-1 in R n is equal to n.

KW - Complex conference matrices

KW - Equi-isoclinic planes

UR - https://www.scopus.com/pages/publications/85051719207

U2 - 10.1007/s13366-017-0374-2

DO - 10.1007/s13366-017-0374-2

M3 - Article

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VL - 59

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JO - Beiträge zur Algebra und Geometrie = Contributions to Algebra and Geometry

JF - Beiträge zur Algebra und Geometrie = Contributions to Algebra and Geometry

IS - 3

ER -

Complex conference matrices and equi-isoclinic planes in Euclidean spaces

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