Find the minimal polynomial given
where
=(x+y,x-y).)
I found the associated matrix, which is
![A=\left[\begin{array}{rr}1&1\\1&-1\end{array}\right].](http://latex.codecogs.com/png.latex?A=\left[\begin{array}{rr}1&1\\1&-1\end{array}\right].)
Now I need to compute the characteristic polynomial, and this is
-1=\lambda ^{2}-2=\big(\lambda-\sqrt2\big)\big(\lambda+\sqrt2\big).)
Now suppose I take
=\lambda-\sqrt2)
then I make
,)
if this is zero, then that polynomial is the minimal one right? If is not zero, then I consider the characteristic polynomial, and that's actually the minimal polynomial because of simple application of Cayley - Hamilton Theorem.
== Yup, but in fact it's easier: since the minimal and the char. polynomials have the same irreducible factors, you know the min. pol. = the char. pol. in this case!
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Another question I have, suppose we're computing the characteristic polynomial, when is it equal to the minimal one?
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Originally Posted by Astrid 
