ESPACIOS VECTORIALES CON PRODUCTO INTERIOR Producto Interior en espacios vectoriales. Propiedades. Norma de vectores en espacios con producto interior. Vectores ortogonales. Bases Ortonormales. Proceso de ortonormalización de bases. Aplicaciones a la geometría
No Thumbnail Available
Date
2021-09-15
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad Nacional de Educación Enrique Guzmán y Valle
Abstract
El objetivo de este trabajo de investigación es abarcar la temática espacial de vectores a la par de
los productos internos, ha sido elaborado con el objetivo, en primer lugar, de conseguir el
grado de Licenciado en Matemática mediante la modalidad de suficiencia. A partir de
estas consideraciones, para el desarrollo de los contenidos de la monografía, se realizó una
breve revisión de las definiciones más logradas y exactas sobre espacios vectoriales,
dependencia, combinación e independencia lineales, así como sobre las dimensiones de
espacios vectoriales y sus bases conceptuales.
A nivel del contenido, la investigación se desarrolla alrededor de la discusión y
contrastación sobre el producto interno, por añadidura, de todos sus elementos o
características que lo configuran como la norma vectorial, desigualdad Schwartz y la
triangular, axiomas, el análisis de la medida angulada producto de la concordancia de dos
vectores, y el producto interno, uno de los ejes operacionales de este trabajo. Por último, se
abarca las nociones detalladas en torno a la ortonormalidad vectorial o de vectores y la
ortogonalidad.
El estudio de dichos conceptos es fundamental por sus múltiples aplicaciones para
un desempeño competente y eficiente de la docencia en la especialidad de matemáticas,
dirigido a los estudiantes de nivel secundario, pero también incluye diversas áreas de
formación profesional universitaria.
Finalmente, deseamos que el presente trabajo monográfico sea de suma importancia
para los estudiantes y docentes del campo de las matemáticas.
The objective of this research work is to cover the spatial theme of vectors along with internal products, it has been elaborated with the objective, first of all, of obtaining the degree of Bachelor of Mathematics through the sufficiency modality. Based on these considerations, for the development of the contents of the monograph, a brief review of the most successful and exact definitions on vector spaces, linear dependence, combination and independence was made, as well as on the dimensions of vector spaces and their bases. conceptual. At the content level, the research is developed around the discussion and contrasting of the internal product, in addition, of all its elements or characteristics that configure it such as the vector norm, Schwartz and triangular inequality, axioms, the analysis of the measure angulated product of the concordance of two vectors, and the internal product, one of the operational axes of this work. Finally, detailed notions about vector or vector orthonormality and orthogonality are covered. The study of these concepts is essential due to its multiple applications for a competent and efficient teaching performance in the specialty of mathematics, aimed at secondary level students, but also includes various areas of university professional training. Finally, we want this monographic work to be of the utmost importance for students and teachers in the field of mathematics.
The objective of this research work is to cover the spatial theme of vectors along with internal products, it has been elaborated with the objective, first of all, of obtaining the degree of Bachelor of Mathematics through the sufficiency modality. Based on these considerations, for the development of the contents of the monograph, a brief review of the most successful and exact definitions on vector spaces, linear dependence, combination and independence was made, as well as on the dimensions of vector spaces and their bases. conceptual. At the content level, the research is developed around the discussion and contrasting of the internal product, in addition, of all its elements or characteristics that configure it such as the vector norm, Schwartz and triangular inequality, axioms, the analysis of the measure angulated product of the concordance of two vectors, and the internal product, one of the operational axes of this work. Finally, detailed notions about vector or vector orthonormality and orthogonality are covered. The study of these concepts is essential due to its multiple applications for a competent and efficient teaching performance in the specialty of mathematics, aimed at secondary level students, but also includes various areas of university professional training. Finally, we want this monographic work to be of the utmost importance for students and teachers in the field of mathematics.
Description
Keywords
Rendimiento académico
Citation
Horostegui Lopez, F. (2021). ESPACIOS VECTORIALES CON PRODUCTO INTERIOR Producto Interior en espacios vectoriales. Propiedades. Norma de vectores en espacios con producto interior. Vectores ortogonales. Bases Ortonormales. Proceso de ortonormalización de bases. Aplicaciones a la geometría (Monografía de pregrado). Universidad Nacional de Educación Enrique Guzmán y Valle, Lima, Perú.