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define a field and its characteristic
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define linear independence, spanning, basis and dimension
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define a linear transformation/map, and an isomorphism
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define a ring and a commutative ring
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define a ring homomorphism and a ring isomorphism
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what is the division algorithm for polynomials
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what is the first isomorphism theorem (ring form)
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Proposition 2.11. Let a, b ∈ F[x] be non-zero polynomials and let gcd(a, b) = c. Then...
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define minimal polynomial of A
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define characteristic polynomial of A
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define eigenvalue, eigenvector
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define minimal polynomial of T
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define characteristic polynomial of T
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define algebraically closed
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what is the fundamental theorem of algebra
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define an algebraic closure of F
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First Isomorphism theorem (quotient space form)
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rank-nullity theorem (quotient space form)
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