Any linearly independent set can be expanded to a basis for the (sub)space

Created almost 9 years ago, updated about 8 hours ago

In a finite-dimensional vector space, any independent list can be extended to a basis. If it does not span, adjoin a vector outside its span; independence is preserved. Each step increases the list size, so the procedure terminates at the dimension of the space. A subspace version uses vectors from that subspace.

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