- (introduction)
- (vector spaces)
- (def)
- (theorem 1)
- (examples of vector spaces)
- (space Rn)
- (polynomial space P(t))
- (polynomial space Pn(t))
- (matrix space Mmn)
- (function space F(x))
- (fields and subfields)
- (linear combinations, spanning sets)
- (example 1,2)
- (spanning sets)
- (example 3, 4, 5)
- (subspaces)
- (def)
- (theorem 2)
- (example 6, 7)
- (intersection of spaces)
- (theorem 3)
- (solution space of a homogeneous system)
- (theorem 4)
- (linear span, row space of matrix)
- (theorem 5)
- (example 8)
- (row space of a matrix)
- (theorem 6, 7, 8, 9)(corollary)(example 9)
- (linear dependence or independence)
- (def)
- (example 10)
- (linear dependence in R3)
- (linear dependence and linear combinations)
- (lemma 10)
- (linear dependence and echelon matrices)
- (theorem 11)
- (basis and dimension)
- (def A)
- (def B)
- (theorem 12)
- (lemma 13)
- (examples of basis)
- (vector space Kn)
- (vector space M=Mrs of all rs matrices)
- (vector space Pn(t) of all polynomials degree <= n)
- (vector space Pn(t) of all polynomials)
- (theorem of basis)
- (theorem 14, 15, 16)
- (example 11)
- (dimensions and subspaces)
- (theorem 17)
- (example 12)
- (application of matrix, rank of a matrix)
- (sums and direct sums)
- (coordinates)
(introduction)(vector space)
(examples of vector space)
(linear combinations, spanning sets)
(subspaces)
(linear span, row space of matrix)
(linear dependence or independence)
(basis and dimension)
(application of matrix, rank of a matrix)
(sums and direct sums)
(coordinates)
(solved problems)
(supplementary problems)
(answers to supplementary problems)
(examples of vector space)
(linear combinations, spanning sets)
(subspaces)
(linear span, row space of matrix)
(linear dependence or independence)
(basis and dimension)
(application of matrix, rank of a matrix)
(sums and direct sums)
(coordinates)
(solved problems)
(supplementary problems)
(answers to supplementary problems)
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