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2d
comment Why do we need to specify the domain of an unbounded operator?
There must be a missing assumption here. If you take a densely defined linear map you could extend it to be defined on the whole space using Zorn's lemma.
2d
comment Why do we need to specify the domain of an unbounded operator?
@user1952009 If your operator $T$ is not closed then it is possible for $x_n \rightarrow x$ such that $\| Tx_n\| \rightarrow \infty$, but $Tx$ is still defined.
Feb
10
comment Cross product and matrix of rotation
What do you mean by extract $\omega$ to the RHS? You only have an expression, not an equation.
Feb
10
comment How can I show that for matrix $A$ , $A^t A $ is not equal to $ A A^t $ in general?
Try writing down a matrix $A$ and testing it out. You're trying to exhibit a counterexample, so it just comes down to finding a matrix $A$ that breaks the claimed identity.
Feb
10
revised Showing a function is differentiable at $x$.
added 5 characters in body
Feb
10
answered Showing a function is differentiable at $x$.
Feb
10
comment If $f: \mathbb{C} \rightarrow \mathbb{C}$ is analytic and $\lim_{z \to \infty} f(z) = \infty$ show that $f$ is a polynomial
@RobArthan $g$ doesn't have a removable singularity, it has a pole, but yes, that requires some knowledge about why it can't be an essential singularity (Casorati-Weierstrass would suffice). But based on the original question it sounds like the OP was aware of that conclusion.
Feb
9
answered If $f: \mathbb{C} \rightarrow \mathbb{C}$ is analytic and $\lim_{z \to \infty} f(z) = \infty$ show that $f$ is a polynomial
Feb
9
answered An equivalent theorem for Sobolev spaces in infinite dimensions
Jan
22
comment Evaluate complex integral using deformation theorem
Hint: You can evaluate the circle integral (integral about $\gamma$) directly by parametrizing the circle.
Jan
21
comment Prove that $W = \{u = (x, y): y = 5x\}$ is a subspace of $\mathbb R^2$. Interpret $W$ geometrically. What's the dimension of $W$?
@user306944, every vector space is a linearly dependent set.
Jan
21
comment Prove that $W = \{u = (x, y): y = 5x\}$ is a subspace of $\mathbb R^2$. Interpret $W$ geometrically. What's the dimension of $W$?
This looks fine. Depending on who is teaching your course, they may be a little bit pedantic about showing explicitly that $0 \in W$. Also, be explicit about determining the dimension of a subspace. For example, you could write down a basis for $W$, and count the number of basis vectors. Because often it is not obvious what the dimension of a space is without doing some computations.
Jan
17
answered How to find “unique” eigenvalues when computed numerically?
Dec
31
awarded  Yearling
Dec
10
comment How to compute this integral
If I use the word "residue" does that put you in the right direction?
Dec
9
comment No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
Your proof does not fail; you observed that $1/f$ is analytic and $|1/f|$ obtains a strict max at $z = 0$, which is impossible.
Dec
9
comment No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
You seem to be missing some words. "contradiction the fact the $f$ isn't". The only thing I can point out is that you don't need to discuss anything about $f$ obtaining a max; all that matters is $1/f$.
Dec
1
comment How do I do a finite expansion of $\int e^{x^2} \, dx$?
We typically say "expressed in terms of elementary functions" instead of "finite expression" because otherwise you could just say that $\mathrm{erf}(x)$ (times some constant) is a finite expression for the antiderivative.
Dec
1
comment Euler differential equations
Do you know the "Method of Undetermined Coefficients"? It can be applied to determine the solution to the inhomogeneous problem.
Nov
23
reviewed Approve $P = \{x \in \Bbb R^n \mid x \cdot v = 0\}$ is a subspace of $\Bbb R^n$