Simultaneous orthogonalization of inner products over arbitrary fields.
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We give necessary and sufficient conditions for a family of inner products in a finite-dimensional vector space V over an arbitrary field K to have an orthogonal basis relative to all the inner products. Some applications to evolution algebras are also considered.
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Yolanda Cabrera Casado, Cristóbal Gil Canto, Dolores Martín Barquero y Cándido Martín González. Simultaneous orthogonalization of inner products over arbitrary fields. Non-Associative Algebras and Related Topics. NAART 2020, pages 213-230. Springer Proceedings in Mathematics & Statistics, vol 427. Springer, Cham. (2023).