Report
Simultaneous orthogonalization of inner products in infinite-dimensional vector spaces
| العنوان: | Simultaneous orthogonalization of inner products in infinite-dimensional vector spaces |
|---|---|
| المؤلفون: | Casado, Yolanda Cabrera, Canto, Cristóbal Gil, Barquero, Dolores Martín, González, Cándido Martín |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Rings and Algebras, 15A63, 11E04 |
| الوصف: | For an arbitrary field $\mathbb{K}$ and a family of inner products in a $\mathbb{K}$-vector space $V$ of arbitrary dimension, we study necessary and sufficient conditions in order to have an orthogonal basis relative to all the inner products. If the family contains a nondegenerate element plus a compatibility condition, then under mild hypotheses the simultaneous orthogonalization can be achieved. So we investigate several constructions whose purpose is to add a nondegenerate element to a degenerate family and we study under what conditions the enlarged family is nondegenerate. Comment: 23 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2107.08705 |
| رقم الانضمام: | edsarx.2107.08705 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |