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High Quality Content by WIKIPEDIA articles! In mathematics, a Schauder basis or countable basis is similar to the usual (Hamel) basis of a vector space; the difference is that for Hamel bases we use linear combinations that are finite sums, while for Schauder bases they may be infinite sums. This makes Schauder bases more suitable for the analysis of infinite-dimensional topological vector spaces including Banach spaces. Schauder bases were described by Juliusz Schauder in 1927, although such bases were discussed earlier (for example, the Haar basis was given in 1909).