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arXiv · 2407.13713

Orthogonality of bilinear forms and application to matrices

Saikat Roy·Tanusri Senapati·Debmalya Sain
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Abstract

We characterize Birkhoff-James orthogonality of continuous vector-valued functions on a compact topological space. As an application of our investigation, Birkhoff-James orthogonality of real bilinear forms are studied. This allows us to present an elementary proof of the well-known Bhatia-\v{S}emrl Theorem in the real case.

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Saikat Roy, Tanusri Senapati, Debmalya Sain. 2024-07-18. Orthogonality of bilinear forms and application to matrices. https://doi.org/10.1016/j.laa.2020.12.032

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