Math 487, 9.19

Continuing along DiAngelo’s script, ch. 1.

  • Linear combinations of a collection of vectors. Linear span.
  • Linear independence. Examples (polynomials, exponentials).
  • Notion of a basis in a linear space. Examples.
  • Theorem: any two bases in a linear space have the same size (called dimension).
  • Rank of a linear operator is the dimension of its image.
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