Abstract
If A and B are non-empty subsets of a vector space V over a field F then the subspace spanned by A ∪ B, i.e. the smallest subspace of V that contains both A and B, is the set of linear combinations of elements of A ∪ B. In other words, it is the set of elements of the form
where a i ∈ A, b j ∈ B, and λ i , µ j ∈ F. In the particular case where A and B are subspaces of V we have \( \sum\limits_{i = 1}^m {{\lambda _i}} {a_i} \in A \) and \( \sum\limits_{j = 1}^n {{\mu _j}} {b_j} \in B \), so this set can be described as
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© 2002 Springer-Verlag London Limited
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Blyth, T.S., Robertson, E.F. (2002). Direct Sums of Subspaces. In: Further Linear Algebra. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-0661-6_3
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DOI: https://doi.org/10.1007/978-1-4471-0661-6_3
Publisher Name: Springer, London
Print ISBN: 978-1-85233-425-3
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