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  • Coordinate vector spaces
  • Abstract vector spaces

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  • Algebraic properties of R^n (or C^n)
  • Axioms of a vector space
  • Spans
  • Linear (in)dependence
  • Bases
  • Dimension
  • Linear transformations
  • Definition and terminology
  • Linear combinations
  • Subspaces
  • Basic properties
  • Isomorphism
  • Geometric properties of R^n (or C^n)
  • Orthogonality and projection

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  • Definition of linear combination of vectors
  • Example of linear combination of vectors in R^2
  • Definition of weights in a linear combination of vectors
  • Example of writing a given vector in R^3 as a linear combination of given vectors
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  1. Linear combinations

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  • Definition of linear combination of vectorsClose match
  • Example of linear combination of vectors in R^2Close match
  • Vector spacesClose match
  • Linear (in)dependenceClose match
  • Linear transformationsClose match
  • BasesClose match
  • SpansClose match
  • Axioms of a vector spaceClose match
  • Example of writing a given vector in R^3 as a linear combination of given vectorsClose match
  • Linear algebraClose match
  • A linear system is equivalent to a vector equation.Close match
  • Coordinate vector spacesClose match
  • Abstract vector spacesClose match
  • Definition of linearly independent set of vectors: if a linear combination is 0Close match
  • A linear transformation of a linear combination is the linear combination of the linear transformationClose match
  • Definition of linear dependence relation on a set of vectorsClose match
  • A vector can be written uniquely as a linear combination of vectors from independent subspaces.Close match
  • Definition of weights in a linear combination of vectorsClose match
  • Definition and terminologyClose match
  • Vector form of solutions to a consistent linear systemClose match

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