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1d
answered Eigenvalues of different symmetric $(2n+1)\times(2n+1)$ matrix
1d
comment Eigenvalues of different symmetric $(2n+1)\times(2n+1)$ matrix
@EFmiza If you row reduce the matrix, $2n-1$ rows become immediately zero.
1d
answered Eigenvalues of different symmetric $(2n+1)\times(2n+1)$ matrix
2d
comment Prove that $f=x^6+ax+5$ is reducible over $\mathbb{Z_7},\forall a\in\mathbb{Z_7}$
@LinusS. I missed the easier one :)
May
27
answered Prove that $f=x^6+ax+5$ is reducible over $\mathbb{Z_7},\forall a\in\mathbb{Z_7}$
May
27
comment Find all continuous real valued function such that $(f(x))^2+C=\int\limits_0^xf(t)dt$
How do you know that $f$ is differentiable?
May
24
comment Fields of arbitrary cardinality
@user28111 I thought that given an infinite set $X$ to prove that the set of strings of finite length in $X$ has the same cardinality one needs choice. Are you sure you don't?
May
24
revised Fields of arbitrary cardinality
edited body
May
24
answered Fields of arbitrary cardinality
May
24
answered Derivatives problem
May
23
answered Is there another way to solve this Trigo in series?
May
23
answered Determining whether or not an element is integral over $\mathbb Z$
May
18
comment Find the eigenvalues for a matrix which is a product of matrices
@Xenomorph Since $A_2$ is diagonal, its eigenvectors are $e_1, e_2$. Now, if $v$ is an eigenvector of $A_1A_2A_1^{-1}$ we have $$A_1A_2A_1^{-1}v= \lambda v \Rightarrow A_2 (A_1^{-1}v)= \lambda A_1^{-1}v $$ This shows that $A_1^{-1}v$ is an eigenvector for $A_2$ or equivalently that $$v= A_1u$$ where $u$ is an eigenvector for $A_2$.
May
18
answered An example of a mapping $\eta\colon\mathbb{N}\to\mathbb{N}$ such that $\eta(x)=n$ has infinitely many solutions for each $n\in\mathbb{N}$
May
18
comment Find the eigenvalues for a matrix which is a product of matrices
@Xenomorph There was a typo, fixed it. Just make $A_1$ a common factor on the left and $A_1^{-1}$ a common factor on the right.
May
18
revised Find the eigenvalues for a matrix which is a product of matrices
added 1 character in body
May
18
answered Find the eigenvalues for a matrix which is a product of matrices
May
18
comment Proving that if $f$ is continuous then $f(a_n)$ converges
@trfv You don't even need the $f(0)=f(1)$ condition. Once you prove that $f(x)$ is constant on $[0,1)$, you just take $x_n \in [0,1)$ which converge to $1$ and use $f(1)=\lim_n f(x_n)$.
May
18
comment Proving that if $f$ is continuous then $f(a_n)$ converges
@Kmt I was answering the question in the comment which is a completely different question. In that question we don't know that $f(0)=f(1)$....
May
18
comment Proving that if $f$ is continuous then $f(a_n)$ converges
@trfv If $f$ is not continuous, this is not true.