jaj•a•person's notes

Steven Roman

Advanced Linear Algebra

10.1007/978-0-387-72831-5

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  • An algebraic element is invertible iff its minimal polynomial has a nonzero constant term
  • Dimension of a vector space
  • Direct sum of vector spaces
  • Every vector space has a basis
  • Rank-nullity theorem
  • Roots of a minimal polynomial
  • Spectral mapping theorem
  • Spectrum of an algebraic element
  • Subalgebra generated by an algebraic element
  • Upper bound on the cardinality of an arbitrary union
  • Vector basis
  • Vector space
  • Vector subspace
  • Zorn's lemma

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