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Embedding and Extension Properties of Hadamard Matrices Revisited

Journal Article


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Abstract


  • © 2018 2018. Hadamard matrices have many applications in several mathematical areas due to their special form and the numerous properties that characterize them. Based on a recently developed relation between minors of Hadamard matrices and using tools from calculus and elementary number theory, this work highlights a direct way to investigate the conditions under which an Hadamard matrix of order n - k can or cannot be embedded in an Hadamard matrix of order n. The results obtained also provide answers to the problem of determining the values of the spectrum of the determinant function for specific orders of minors of Hadamard matrices by introducing an analytic formula.

UOW Authors


  •   Christou, Dimitrios (external author)
  •   Mitrouli, Marilena (external author)
  •   Seberry, Jennifer

Publication Date


  • 2018

Citation


  • Christou, D., Mitrouli, M. & Seberry, J. (2018). Embedding and Extension Properties of Hadamard Matrices Revisited. Special Matrices, 6 (1), 155-165.

Scopus Eid


  • 2-s2.0-85045953680

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2374&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/1372

Number Of Pages


  • 10

Start Page


  • 155

End Page


  • 165

Volume


  • 6

Issue


  • 1

Abstract


  • © 2018 2018. Hadamard matrices have many applications in several mathematical areas due to their special form and the numerous properties that characterize them. Based on a recently developed relation between minors of Hadamard matrices and using tools from calculus and elementary number theory, this work highlights a direct way to investigate the conditions under which an Hadamard matrix of order n - k can or cannot be embedded in an Hadamard matrix of order n. The results obtained also provide answers to the problem of determining the values of the spectrum of the determinant function for specific orders of minors of Hadamard matrices by introducing an analytic formula.

UOW Authors


  •   Christou, Dimitrios (external author)
  •   Mitrouli, Marilena (external author)
  •   Seberry, Jennifer

Publication Date


  • 2018

Citation


  • Christou, D., Mitrouli, M. & Seberry, J. (2018). Embedding and Extension Properties of Hadamard Matrices Revisited. Special Matrices, 6 (1), 155-165.

Scopus Eid


  • 2-s2.0-85045953680

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2374&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/1372

Number Of Pages


  • 10

Start Page


  • 155

End Page


  • 165

Volume


  • 6

Issue


  • 1