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How to find Minimal Polynomial | Field Theory
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Here in this video we see the definition of minimal polynomial but before going to this topic we need to first understand the theorem from which this concept is introduced.
This theorem simply states that
Let E be an algebraic extension of field F and let u be an algebraic element over F. Then there exist a polynomial of least degree p(x) then
i) This p(x) is irreducible over F.
ii) let g(x) be another polynomial such that u is root of it i.e . g(u)=0
then p(x) | g(x) ( p(x) divides g(x).
iii) There exists a unique monic irreducible polynomial .
This p(x) is Minimal polynomial.
Here we also find the minimal polynomial corresponding to algebraic element.
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