Steven Roman

Advanced linear algebra

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