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Definition of spanning/generating set for a space or subspace

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A set of vectors containing fewer elements than the dimension of the space cannot span

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A set of vectors containing fewer elements than the dimension of the space cannot span

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Definition of spanning/generating set for a space or subspaceClose match
If a vector space has dimension nClose match
Definition of span of a set of vectorsClose match
SpansClose match
A set of nonzero vectors contains (as a subset) a basis for its span.Close match
A set of vectors containing more elements than the dimension of the space must be linearly dependentClose match
Definition of subspace spanned by a set of a set of vectorsClose match
The span of a set of vectors is a subspaceClose match
Definition of dimension of a vector space (or subspace) being finite or infiniteClose match
Geometric description of span of a set of vectors in R^n (or C^n)Close match
Every basis for a vector space contains the same number of elementsClose match
Definition of dimension of a vector space (or subspace)Close match
A set is a basis if each vector can be written uniquely as a linear combination.Close match
Definition of basis of a vector space (or subspace)Close match
Removing a linearly dependent vector from a set does not change the span of the set.Close match
Determine if a particular set of vectors spans R^3Related
The dimension of a subspace is less than or equal to the dimension of the whole spaceRelated
Determine if a particular vector is in the span of a set of vectorsRelated
Determine if a particular vector is in the span of a set of vectors in R^2Related
Determine if a particular vector is in the span of a set of vectors in R^3Related

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