Are infinite-dimensional vector spaces systematically and rigorously discussed in any linear algebra text(s)?
If so, please give a few here, as well as any courses with online content taught using that (those) text(s).
2026-03-31 21:07:11.1774991231
Any linear algebra texts on infinite-dimensional vector spaces?
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They're often covered in textbooks on functional analysis with added structure, i.e. a norm, completeness, or an inner product. You could try Rudin's Real and Complex Analysis for the basics of infinite dimensional vector spaces and Conway's A Course on Functional Analysis covers more.
Linear algebra textbooks don't typically discuss much of the infinite dimensional case, but many of the basics of linear algebra extend to the infinite dimensional case pretty straightforwardly, e.g. inner product spaces have basically the same proofs in finite or infinite dimensions.