Simultaneous orthogonalization of inner products in infinite-dimensional vector spaces - Cabrera-Casado, Yolanda; Gil-Canto, Cristóbal; Martín-Barquero, Dolores; Martín-González, Cándido (Taylor and Francis, 2025)
For an arbitrary field K and a family of inner products in a K-vector space V of arbitrary dimension, we study necessary and sufficient conditions in order to have a basis which is orthogonal 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.
https://openpolicyfinder.jisc.ac.uk/id/publication/5818
Keywords: Álgebra lineal; Análisis numérico; Inner product; Simultaneous orthogonalization; Simultaneous diagonalization