Some properties of Hadamard matrices generated recursively by Kronecker products

Benjamin Arazi

doi:10.1016/0024-3795(79)90003-X

Some properties of Hadamard matrices generated recursively by Kronecker products

Benjamin Arazi

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

3 Scopus citations

Abstract

A natural Hadamard matrix H_n is a 2ⁿ × 2ⁿ matrix defined recursively as H_n+1= 1 1 1 -1⊗ H_n, where ⊗ denotes the Kronecker product. Some properties of such matrices which follow from the above definition are shown in this paper. These include a certain relation between defined reduction and expansion properties, parity considerations in the Hadamard domain and some dyadic properties.

Original language	English
Pages (from-to)	27-39
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	25
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(79)90003-X
State	Published - 1 Jan 1979
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/0024-3795(79)90003-X

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title = "Some properties of Hadamard matrices generated recursively by Kronecker products",

abstract = "A natural Hadamard matrix Hn is a 2n × 2n matrix defined recursively as Hn+1= 1 1 1 -1⊗ Hn, where ⊗ denotes the Kronecker product. Some properties of such matrices which follow from the above definition are shown in this paper. These include a certain relation between defined reduction and expansion properties, parity considerations in the Hadamard domain and some dyadic properties.",

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N2 - A natural Hadamard matrix Hn is a 2n × 2n matrix defined recursively as Hn+1= 1 1 1 -1⊗ Hn, where ⊗ denotes the Kronecker product. Some properties of such matrices which follow from the above definition are shown in this paper. These include a certain relation between defined reduction and expansion properties, parity considerations in the Hadamard domain and some dyadic properties.

AB - A natural Hadamard matrix Hn is a 2n × 2n matrix defined recursively as Hn+1= 1 1 1 -1⊗ Hn, where ⊗ denotes the Kronecker product. Some properties of such matrices which follow from the above definition are shown in this paper. These include a certain relation between defined reduction and expansion properties, parity considerations in the Hadamard domain and some dyadic properties.

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U2 - 10.1016/0024-3795(79)90003-X

DO - 10.1016/0024-3795(79)90003-X

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JO - Linear Algebra and Its Applications

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ER -

Some properties of Hadamard matrices generated recursively by Kronecker products

Abstract

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