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 Yearling
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Mar
31
comment Problems with votes
please complete the question
Mar
31
accepted Polynomials vanishing and non-intersecting varieties.
Mar
31
asked Polynomials vanishing and non-intersecting varieties.
Mar
29
comment A linear subspace of projective space
Is it easy to show that the "biggest" linear proper linear subspace is a hyperplane? And thus, by what you've shown since it cannot be contained in that, it must be the whole thing?
Mar
29
comment A linear subspace of projective space
how do we know there cannot be more than one hyperplane? is the span of two distinct hyperplanes the whole space necessarily?
Mar
29
asked A linear subspace of projective space
Mar
25
accepted Do complex eigenvalues of a real matrix imply a rotation-dilation?
Mar
25
comment Do complex eigenvalues of a real matrix imply a rotation-dilation?
I see what you mean. My above method is correct too, right?
Mar
25
comment Do complex eigenvalues of a real matrix imply a rotation-dilation?
Are the two $\lambda$ different? Just say $v=cw$ where $c$ is real nonzero. Then we have that $av-bw=L(v)=L(cw)=c(bv+aw)$. Then what do I take the difference of? I am just saying $0=L(v-cw)=(av-bw)-c(bv+aw)=(a-bc)v-(b+ca)w=(a-bc)cw-(b+ca)w=(ac-bc^2)w-(b+ca)w=‌​(-b-bc^2 )w=0$. So $b=-bc^2$. If $b\neq0$ then $c^2=-1$, a contradiction to $c$ is real.
Mar
25
comment Do complex eigenvalues of a real matrix imply a rotation-dilation?
I don't know if what I said made sense, sorry. Could you just elaborate briefly on the implication from $b\neq0$ to $v,w$ being linearly independent over the reals.
Mar
25
comment Do complex eigenvalues of a real matrix imply a rotation-dilation?
Sorry, why must they be linearly independent over the real numbers? Is it because if they weren't then $cv=w$ for real $c$ and thus multiplying them by a complex number $\lambda$ just had the effect of a real scalar since it would $(av-bcv,bv+acv)=((a-bc)v,(b+cv)v)$ where $a,b,c$ are real numbers?
Mar
25
revised Do complex eigenvalues of a real matrix imply a rotation-dilation?
added 5 characters in body; edited title
Mar
23
comment Do complex eigenvalues of a real matrix imply a rotation-dilation?
Thank you for the help. A couple clarification questions: 1) What do you mean in 5. by real and imaginary parts of $v$? Do you mean writing $v$ as $x+iy$ where $x,y$ are real vectors and looking at the span of ${x,y}$ with the scalar field being $C$? 2) In 6. when you say likewise for $-i(v-\bar v)$ are you just saying $A^n(-i(v-\bar v))= -iA^n(v-\bar v)=-i(\lambda^nv-\bar\lambda^n\bar v)$. So what? 3) In 6. again, what is this point in $K$? It seems like we are only talking about complex vectors.
Mar
23
revised Do complex eigenvalues of a real matrix imply a rotation-dilation?
added 16 characters in body
Mar
23
comment Do complex eigenvalues of a real matrix imply a rotation-dilation?
I don't quite follow. We want to assume that $0\in int(K)$ so having this fixed point doesn't really seem to help.
Mar
23
asked Do complex eigenvalues of a real matrix imply a rotation-dilation?
Mar
22
comment Is primitivity invariant under matrix conjugation.
O ok. I see, sorry. Let me rephrase my question though.
Mar
22
asked Is primitivity invariant under matrix conjugation.
Mar
17
awarded  Yearling
Feb
25
accepted Subspace of Noetherian space still Noetherian