Basis for a Vector Space, Coordinate Vector Relative to Basis - Linear Algebra

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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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