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arXiv · 2107.08705

Simultaneous orthogonalization of inner products in infinite-dimensional vector spaces

Yolanda Cabrera Casado·Cristóbal Gil Canto·Dolores Martín Barquero·Cándido Martín González
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Abstract

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.

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Yolanda Cabrera Casado, Cristóbal Gil Canto, Dolores Martín Barquero, Cándido Martín González. 2021-07-19. Simultaneous orthogonalization of inner products in infinite-dimensional vector spaces. https://arxiv.org/abs/2107.08705

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