Part A Linear Algebra

define a field and its characteristic

define a vector space

define linear independence, spanning, basis and dimension

define a linear transformation/map, and an isomorphism

define a ring and a commutative ring

define a ring homomorphism and a ring isomorphism

define an ideal

what is the division algorithm for polynomials

what is the first isomorphism theorem (ring form)

Proposition 2.11. Let a, b ∈ F[x] be non-zero polynomials and let gcd(a, b) = c. Then...

define minimal polynomial of A

define characteristic polynomial of A

define eigenvalue, eigenvector

define minimal polynomial of T

define characteristic polynomial of T

define algebraically closed

what is the fundamental theorem of algebra

define an algebraic closure of F

define quotient space

First Isomorphism theorem (quotient space form)

rank-nullity theorem (quotient space form)