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11h
comment How can I show that for matrix $A$ , $A^t A $ is not equal to $ A A^t $ in general?
Please check your TeX code.
11h
answered How can I show that for matrix $A$ , $A^t A $ is not equal to $ A A^t $ in general?
14h
awarded  Nice Answer
15h
answered $\int_{0}^{10} \int_{0}^{10} \int_{0}^{10} (x+y+z)$
1d
comment $\text{Hom}_{\mathcal{O}_X}(\cdot, \mathcal{G})$ is exact functor
If $\delta_W$ is surjective it is right cancellable.
1d
comment If commutativity of vector space is omitted, can we still use other axioms to prove the commutativity?
(Of course the very same proof applies to prove a ring with unit must have commutative addition)
1d
comment If commutativity of vector space is omitted, can we still use other axioms to prove the commutativity?
@mvw The axiom that the sum in a unital ring is commutative is redundant, but most people don't drop it when defining a unital ring.
2d
comment The matrix $A = (a_{i,j})$ in which $a_{i,j} = 0$ if $i ≥ j$ is nilpotent.
You don't need to calculate eigenvalues, since $\chi(t)=\det(A-tI)$ and since the elements below the diagonal vanish you can expand through the main diagonal and obtain the result.
2d
answered Only two groups of order $10$: $C_{10}$ and $D_{10}$
Feb
7
revised The formula $\DeclareMathOperator{tr}{tr}\mathrm{adj}(A)=\tfrac{1}{2}[(\tr A)^2-\tr(A^2)]I_3-[\tr A]A+A^2$ for the adjoint of a $3\times 3$ matrix
edited title
Feb
6
comment Groups isomorphic to $S_{4}/N$
This was asked a few days ago.
Feb
6
comment If an R-module P is free and A and B are direct summands of P then A∩B is isomorphic to a direct summand of P? is it true? I could not prove it?
Are you assuming anything on $R$?
Feb
6
comment Given a normal $A_{n\times n}$ matrix, then $\lVert A^*v \rVert = \lVert Av\rVert$ and $\langle Av,v\rangle = \langle A^*v,v\rangle$
@kuhaku The definition of the adjoint $A^\ast$ of $A$ is that for any vectors $v,w$, $\langle Av,w\rangle =\langle v,A^\ast w\rangle$. (If my answer didn't clear things up for you, it is not useful to accept it. You can always wait for other answers.)
Feb
6
answered Given a normal $A_{n\times n}$ matrix, then $\lVert A^*v \rVert = \lVert Av\rVert$ and $\langle Av,v\rangle = \langle A^*v,v\rangle$
Feb
4
comment Find an infinite collection of maximal ideals containing $(x^2 - y^3) \subset \mathbb{C}[x,y]$
@user26857 I just wanted to stress the fact one should think about points in this case, and then it is more or less intuitive why there are infinitely many points: the curve $x^2=y^3$ consists of infinitely many points in $\Bbb C^2$.
Feb
4
answered Determine if quotient group $S_4/N$ is isomophic to $S_3$
Feb
4
answered Find an infinite collection of maximal ideals containing $(x^2 - y^3) \subset \mathbb{C}[x,y]$
Feb
4
comment Find an infinite collection of maximal ideals containing $(x^2 - y^3) \subset \mathbb{C}[x,y]$
Maximal ideals are points. So...?
Feb
4
comment Order-Preserving Bijection $f:A\to A^*$?
The set of words on A is always infinite, so if A is finite there is no hope for a bijection.
Feb
3
comment Algebraic element - integral domain
dependent, not dependant