Embedding and Extension Properties of Hadamard Matrices Revisited
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 highli...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2018-03-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2018-0012 |
| _version_ | 1818689848351916032 |
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| author | Christou Dimitrios Mitrouli Marilena Seberry Jennifer |
| author_facet | Christou Dimitrios Mitrouli Marilena Seberry Jennifer |
| author_sort | Christou Dimitrios |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T12:16:37Z |
| format | Article |
| id | doaj.art-f4c14e91968840d1bcf7b81ba4c8b288 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-17T12:16:37Z |
| publishDate | 2018-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-f4c14e91968840d1bcf7b81ba4c8b2882022-12-21T21:49:10ZengDe GruyterSpecial Matrices2300-74512018-03-016115516510.1515/spma-2018-0012spma-2018-0012Embedding and Extension Properties of Hadamard Matrices RevisitedChristou Dimitrios0Mitrouli Marilena1Seberry Jennifer2Department of Science and Mathematics, Deree -The American College of Greece, 6 Gravias St. GR-15342, Athens, GreeceDepartment of Mathematics, National and Kapodistrian University of Athens, Panepistemiopolis GR-15773, Athens, GreeceSchool of Computing and Information Technology, University of Wollongong, Wollongong NSW 2522, AustraliaHadamard 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.https://doi.org/10.1515/spma-2018-0012submatricesminorsdeterminant spectrumdifferentiation |
| spellingShingle | Christou Dimitrios Mitrouli Marilena Seberry Jennifer Embedding and Extension Properties of Hadamard Matrices Revisited Special Matrices submatrices minors determinant spectrum differentiation |
| title | Embedding and Extension Properties of Hadamard Matrices Revisited |
| title_full | Embedding and Extension Properties of Hadamard Matrices Revisited |
| title_fullStr | Embedding and Extension Properties of Hadamard Matrices Revisited |
| title_full_unstemmed | Embedding and Extension Properties of Hadamard Matrices Revisited |
| title_short | Embedding and Extension Properties of Hadamard Matrices Revisited |
| title_sort | embedding and extension properties of hadamard matrices revisited |
| topic | submatrices minors determinant spectrum differentiation |
| url | https://doi.org/10.1515/spma-2018-0012 |
| work_keys_str_mv | AT christoudimitrios embeddingandextensionpropertiesofhadamardmatricesrevisited AT mitroulimarilena embeddingandextensionpropertiesofhadamardmatricesrevisited AT seberryjennifer embeddingandextensionpropertiesofhadamardmatricesrevisited |