MATH 115AH Lecture 4: Bases
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Dimensional us if , write f- dust if. F a basis with finitely many ett i . e . 0 a finite dimension us of dimension o. S is a basis for span is ) Duh t tdnvn me call ai the coordinates of. B is linearly independent do - fo = o ti i - e di fi ti. V be a vs tf , v , in. Ih can cannot you also start give any special property to n . at. V can be spanned by a finite number of elements. Sun , then a subset of su , . vn is a basis f- dust of v . vn ) we prove the result by induction on n . "s win } form a basis for v. Until is linearly independent , hmearlydependent may assume it"s done . Changing notation we may assume dwuto so ain"t, exists.
