Subspaces
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- Definition of subspace
- Definition of subspace spanned by a set of a set of vectors
- Definition of the 0/trivial subspace
- Definition of 0/trivial subspace
- A nonempty subset of a vector space is a subspace if and only if it is closed under linear combinations
- Definition of intersection of subspaces
- The intersection of subspaces is a subspace
- Definition of sum of subspaces
- The sum of subspaces is a subspace
- Definition of direct sum of subspaces
- The dimension of a direct sum of subspaces is the sum of the dimensions of the subspaces.
- Definition of independent subspaces
- A vector can be written uniquely as a linear combination of vectors from independent subspaces.
- The union of bases from independent subspaces is a basis for the space.
- Definition of complement of a subspace
- Theorem characterizing when a space is the direct sum of two subspaces
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