Expression of the 3- and 4-dimensional vectors in total polar exponential form
We express the vectors in R3 and in R4 (M) in terms of square 2x2 matrices. The objective is to write these vectors in a similar way as the complex numbers in C, once considered the isomorphism of R2 with C, with the exponential polar form, including the Euler's formula. In this way we are able...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/8183 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/8183 |
| Access Level: | acceso abierto |
| Palabra clave: | 53 51-73 Formulación matricial Tiempo y espacio Relatividad especial Formula de Euler. Matrix formalism Time and space Special Relativity Euler´s formula Astrofísica Física-Modelos matemáticos Física matemática Álgebra Geometría 1201 Álgebra 1204 Geometría |
| Sumario: | We express the vectors in R3 and in R4 (M) in terms of square 2x2 matrices. The objective is to write these vectors in a similar way as the complex numbers in C, once considered the isomorphism of R2 with C, with the exponential polar form, including the Euler's formula. In this way we are able to write the vectors in R3 and in the Minkowski space M in matrix exponential form and also in an extended polar matrix exponential form. The treatment motivates a digression on the structure of the time and space. |
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