Generating orthogonal bases of R
This thesis presents a solution to the problem of constructing orthogonal bases of the vector space R3 with integer coordinates and integer lengths. Given a vector u, arbitrary integers x and y, the vectors v and w can be obtained and will form an orthogonal basis for R3 of the desired type using th...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
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Animo Repository
1993
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16117 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | This thesis presents a solution to the problem of constructing orthogonal bases of the vector space R3 with integer coordinates and integer lengths. Given a vector u, arbitrary integers x and y, the vectors v and w can be obtained and will form an orthogonal basis for R3 of the desired type using the definitions and theorems mentioned in this study. The researchers provide a review of definitions, theorems and corollaries that are necessary for the discussion of the orthogonal bases of R3 with integer coordinates and integer lengths.All the theorems stated in this study are lifted from the article written by Anthony Osborne and Hans Liebeck (Jan., 1989). The researchers provided complete proofs of the theorems and examples. Other theorems formulated by the researchers were also derived from the article. |
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