Boolean hypercubes and the structure of vector spaces
The present study pretends to describe an alternative way to look at Vector Spaces as a scaffold to produce a meaningful new theoretical structure to be used in both classical and quantum QSPR. To reach this goal it starts from the fact that N-Dimensional Boolean Hypercubes contain as vertices the w...
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| Formaat: | Artikel |
| Taal: | English |
| Gepubliceerd in: |
Mahmut Akyigit
2018-05-01
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| Reeks: | Journal of Mathematical Sciences and Modelling |
| Onderwerpen: | |
| Online toegang: | https://dergipark.org.tr/tr/download/article-file/482652 |
| _version_ | 1827377844486930432 |
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| author | Ramon Carbó-dorca |
| author_facet | Ramon Carbó-dorca |
| author_sort | Ramon Carbó-dorca |
| collection | DOAJ |
| description | The present study pretends to describe an alternative way to look at Vector Spaces as a scaffold to produce a meaningful new theoretical structure to be used in both classical and quantum QSPR. To reach this goal it starts from the fact that N-Dimensional Boolean Hypercubes contain as vertices the whole information maximally expressible by means of strings of N bits. One can use this essential property to construct the structure of $N$-Dimensional Vector Spaces, considering vector classes within a kind of Space Wireframe related to a Boolean Hypercube. This way of deconstruct-reconstruct Vector Spaces starts with some newly coined nomenclature, because, through the present paper, any vector set is named as a Vector Polyhedron, or a polyhedron for short if the context allows it. Also, definition of an Inward Vector Product allows to easily build up polyhedral vector structures, made of inward powers of a unique vector, which in turn one might use as Vector Space basis sets. Moreover, one can construct statistical-like vectors of a given Vector Polyhedron as an extended polyhedral sequence of vector inward powers. Furthermore, the Complete Sum of a vector is defined simply as the sum of all its elements. Once defined, one can use it to compute, by means of inward products, generalized scalar products, generalized vector norms and statistical-like indices attached to a Vector Polyhedron. |
| first_indexed | 2024-03-08T12:46:09Z |
| format | Article |
| id | doaj.art-3ce9b400500641f496bb77ed143751f8 |
| institution | Directory Open Access Journal |
| issn | 2636-8692 |
| language | English |
| last_indexed | 2024-03-08T12:46:09Z |
| publishDate | 2018-05-01 |
| publisher | Mahmut Akyigit |
| record_format | Article |
| series | Journal of Mathematical Sciences and Modelling |
| spelling | doaj.art-3ce9b400500641f496bb77ed143751f82024-01-21T07:26:55ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922018-05-011111410.33187/jmsm.4131161408Boolean hypercubes and the structure of vector spacesRamon Carbó-dorcaThe present study pretends to describe an alternative way to look at Vector Spaces as a scaffold to produce a meaningful new theoretical structure to be used in both classical and quantum QSPR. To reach this goal it starts from the fact that N-Dimensional Boolean Hypercubes contain as vertices the whole information maximally expressible by means of strings of N bits. One can use this essential property to construct the structure of $N$-Dimensional Vector Spaces, considering vector classes within a kind of Space Wireframe related to a Boolean Hypercube. This way of deconstruct-reconstruct Vector Spaces starts with some newly coined nomenclature, because, through the present paper, any vector set is named as a Vector Polyhedron, or a polyhedron for short if the context allows it. Also, definition of an Inward Vector Product allows to easily build up polyhedral vector structures, made of inward powers of a unique vector, which in turn one might use as Vector Space basis sets. Moreover, one can construct statistical-like vectors of a given Vector Polyhedron as an extended polyhedral sequence of vector inward powers. Furthermore, the Complete Sum of a vector is defined simply as the sum of all its elements. Once defined, one can use it to compute, by means of inward products, generalized scalar products, generalized vector norms and statistical-like indices attached to a Vector Polyhedron.https://dergipark.org.tr/tr/download/article-file/482652vector spacesvector semispacesvector polyhedraboolean hypercubesvector space wireframeperfectwhole and hollow vectorscomplete sum of a vectorinward vector productinward vector powerpower basis setsgeneralized scalar productsgeneralized vector normsstatisticallike vectors and indices |
| spellingShingle | Ramon Carbó-dorca Boolean hypercubes and the structure of vector spaces Journal of Mathematical Sciences and Modelling vector spaces vector semispaces vector polyhedra boolean hypercubes vector space wireframe perfect whole and hollow vectors complete sum of a vector inward vector product inward vector power power basis sets generalized scalar products generalized vector norms statisticallike vectors and indices |
| title | Boolean hypercubes and the structure of vector spaces |
| title_full | Boolean hypercubes and the structure of vector spaces |
| title_fullStr | Boolean hypercubes and the structure of vector spaces |
| title_full_unstemmed | Boolean hypercubes and the structure of vector spaces |
| title_short | Boolean hypercubes and the structure of vector spaces |
| title_sort | boolean hypercubes and the structure of vector spaces |
| topic | vector spaces vector semispaces vector polyhedra boolean hypercubes vector space wireframe perfect whole and hollow vectors complete sum of a vector inward vector product inward vector power power basis sets generalized scalar products generalized vector norms statisticallike vectors and indices |
| url | https://dergipark.org.tr/tr/download/article-file/482652 |
| work_keys_str_mv | AT ramoncarbodorca booleanhypercubesandthestructureofvectorspaces |