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1d
comment move curve normal to itself
In the first paragraph you are representing the curve as a graph $y=f(x)$ over the $x$ axis, and in the second paragraph, as an implicit level set $f(x,y) = 0$. Which are you interested in? (Spoiler alert: the answer won't be pleasant in any case.)
1d
comment Probability that a natural number is a sum of two squares?
I see; makes sense.
1d
revised Newton iteration on Riemannian manifolds
added 30 characters in body
1d
answered Newton iteration on Riemannian manifolds
1d
comment Probability that a natural number is a sum of two squares?
Why are the effects of the primes independent? $21$ is spoiled by both $3$ and $7$,won't it be double-counted?
2d
comment Newton iteration on Riemannian manifolds
I think the key point is that Taylor's theorem (and Newton's method) require only differential, and not metric, structure. So you can perform Newton's method on a manifold using any chart; your proposal is to use a chart in normal coordinates. Perhaps this converges faster than using an arbitrary chart, but I have my doubts (I think it strongly depends on the structure of $f$).
2d
reviewed Close Integration question
2d
reviewed Leave Open Least Upper Bound Proof
2d
reviewed Looks OK Upper Bounds and Least Upper Bounds
2d
reviewed Looks OK For each positive integer $a$, does there exist a positive integer $b$ such that $2b^2 + b \gt ab^2$?
2d
reviewed No Action Needed Interpretation of a tail event
2d
reviewed Leave Closed Finding all homomorphisms
Aug
30
comment Solve the following differential equation subject to the specified boundaries:
You made a mistake in the last step. $T$ is 3 at $r=1$, but you used that $T$ is 1 at $r=3$.
Aug
30
comment $m \times n$ matrix gives rise to a well-defined map from $\mathbb{R}^n$ to $\mathbb{R}^m$?
True, although I would argue that $\mathbb{R}^n$ conventionally comes with an implicit Cartesian basis unless otherwise specified.
Aug
29
comment Mean curvature formula of hypersurface in sphere
Can you say a bit more? There exist surfaces of arbitrarily large, and arbitrarily small, intgrated mean curvature that can be isometrically embedded in the unit sphere.
Aug
29
comment Equality of determinants for a specific collection of square matrices of size $n=2^m$
Put differently, $A_q = D_q A D_q$ where $D_q$ is a diagonal matrix of signs (the precise pattern of signs is unimportant).
Aug
29
comment Equality of determinants for a specific collection of square matrices of size $n=2^m$
@PaulSundheim But you are: you pick some subset of the rows, and multiple them all by $-1$. Then you pick the same subset of the columns, and multiply them by $-1$. Each multiplication flips the sign of the determinant.
Aug
29
comment Equality of determinants for a specific collection of square matrices of size $n=2^m$
@PaulSundheim The sign of column $i$ is not the same as that of row $i$? This is true for all of your examples and of your formula for $A_q$, unless I'm misunderstanding.
Aug
29
answered Physical interpretation for the curl of a field
Aug
29
answered Equality of determinants for a specific collection of square matrices of size $n=2^m$