Linear Combination

up:: Vector Space

Given a vector space and a subset , we say that a vector is a linear combination of if there are coefficients in the vector space’s Field such that

That is, can be decomposed into components of the vectors .

Related

• A subset of a vector space is Linearly Dependent if there is at least one vector inside it which is a linear combination of the other vectors
• A subset is Linearly Independent if no vectors inside it are linear combinations of any other vectors.

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References

• Um Curso de Álgebra Linear, Flávio Ulhoa Coelho & Mary Lilian Lourenço. Editora EDUSP.