The span of a subspace is the set of all possible linear combinations of its vectors. It represents the entire space that can be formed using those vectors.
The span of a subspace can be calculated by determining the linear independence of its vectors. If the vectors are linearly independent, then the span is equal to the number of vectors. If the vectors are linearly dependent, then the span is equal to the number of linearly independent vectors.
No, the span of a subspace can be less than or equal to the number of vectors in the subspace. This depends on the linear independence of the vectors in the subspace.
Yes, the span of a subspace can change if the vectors in the subspace are changed or if new vectors are added to the subspace. However, the span will always be a subset of the original subspace.
The span of a subspace is directly related to the dimension of a vector space. The dimension of a vector space is equal to the maximum number of linearly independent vectors that can be formed from the subspace, which is equal to the span of the subspace.