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Jan
22
comment What happens if we change the definition of quotient ring to the one that does not have ideal restriction?
If $I$ is not an ideal then multiplication is not well-defined: you can have $a+I = b+I$ but $(a+I)(c+I) \ne (b+I)(c+I)$.
Jan
21
awarded  Civic Duty
Jan
15
comment In what sense is a pseudo-Riemannian metric a “metric”?
In linear algebra, non-degenerate symmetric bilinear forms are often called "metrics" as well, even though they do not give rise to a metric space in the usual sense. It's just an overuse of the term "metric".
Jan
14
comment Continuity and differentiability relationship
No, that is not enough: a differentiable function need not have continuous partial derivatives. In other words, continuous partial derivatives implies differentiable, but not conversely.
Jan
11
comment What to use for r in proof by contradiction?
To clarify, are you trying to prove that the given claim is true? Why did you decide to do this instead of trying to show it's false?
Dec
28
comment Faulty application of the Fundamental Theorem of Calculus to $f(x) = 0$ for $x\ne 0$, $f(0)=1$
Why is $g$ differentiable?
Dec
28
comment Show $D^2=0$ iff $D=e^{-f}de^{f}$ for some function $f$ , where $D\omega := d\omega+\alpha \wedge \omega $
The first term is a $(k+2)$-form, and is something you can compute further. Can you show that $D^2 = 0$ iff $\alpha$ is closed?
Dec
24
comment Linear independence question (do 2 vectors who are not multiples of one another and a third which is not in their span form R^3?
It doesn't make sense to say that vectors in $\mathbb R^5$ span $\mathbb R^2$ or $\mathbb R^3$.
Dec
18
comment Determinant: Continuity
How are you defining the determinant?
Dec
17
comment Differentiablility of a function
Your use of L'Hopital's rule is invalid: the limit after you differentiate numerator and denominator must exist in order for L'Hopital to be applicable.
Dec
15
comment Complex Analysis using derivatives
I see nothing whatsoever about derivatives in the linked-to article.
Dec
11
comment Restrictive definition of diagonalizable matrix
If every matrix can be "diagonalized" according to your definition, then what is the point of even introducing that definition?
Dec
11
comment Linear transformation ker and image
Neither of your candidate vectors for a basis of the kernel are actually in the kernel.
Dec
10
awarded  Caucus
Dec
5
comment Proof of an inverse
Show that $F$ is bijective.
Dec
5
comment Is a homomorphisim one-to-one or onto?
Smooth functions are continuous, hence any smooth function has an antiderivative.
Dec
5
comment Is a homomorphisim one-to-one or onto?
Hmmm, it seems I deleted my comment by mistake. To recap: the function $f$ defined by $f(x) = \int_0^x e^{t^2}\,dt$ has derivative $f'(x) = e^{x^2}$, and more generally any continuous function has an antiderivative by a similar argument.
Dec
2
comment orthogonal subspaces in $\mathbb R^2$
Your impression is incorrect: a set consisting of a single vector is considered to be orthogonal since it is true that any vector in this set is orthogonal to anything else in it, simply because there is no other vector in the set on which to test this condition.
Dec
1
answered Vector dot product = 0 for perpendicular vectors
Nov
27
comment Triple Integrals: Conversion
You're being asked only to sketch the region of integration, not to actually compute the integral.