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Basis for a Vector Space, Coordinate Vector Relative to Basis - Linear Algebra
5 days ago
32
Science
Education
linear algebra
linear algebra coordinate vector
coordinate vector linear algebra
vector spaces
linear algebra coordinates and basis
change of coordinates linear algebra
basis linear algebra
change of basis linear algebra
basis and dimension of a vector space
Definition and explanation of what a basis is for a vector space using examples (e.g. R3, matrix), including notation or symbol, theorem, properties, span, basis vectors, difference to unit vectors, meaning of e1, e2, standard basis, how to check if vectors are linearly independent, axiom of choice.
0:00 Basis for a vector space, definition
9:00 Vector spaces with no basis
11:44 Basis representation of vectors, uniqueness
14:15 Worked examples
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