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 Pundit
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18h
comment Approximating simple function by continuous function
You're on the right track. Using the result you proved, you know how to approximate each characteristic function. The function you want to approximate is a sum of characteristic functions, so you can approximate that by...
Apr
23
comment Applying Cauchy Residue Theorem
For one thing, the only way for a pole to be "inside" a contour is if the contour is a closed curve.
Apr
23
comment Equivalent definition of bounded set in norm linear space
And what have you tried?
Apr
23
comment Adjoint operator on Banach space
In general it is not true that $T^{\ast \ast} = T$. Are $X,Y$ reflexive spaces?
Apr
22
comment Sufficient conditions on integration kernel for continuity of the integral operator
Where does the $f$ go in the definition of $T$?
Apr
22
reviewed Close Are the only sets in $\mathbb{R^1}$ which are both open and closed $\mathbb{R^1}$ and $\emptyset$?
Apr
22
reviewed Close Group of even order contains an element of order 2
Apr
22
reviewed Close Showing that $\mathbb{R}$ is connected
Apr
22
reviewed Leave Open Is a compact, simply-connected 3-manifold necessarily $S^3$ with $B^3$'s removed?
Apr
22
reviewed Leave Open Probability of a deck of cards
Apr
22
comment Numerical phase plane?
If you do not want to write your own code, you can try downloading the java applet "pplane", which can plot phase diagrams: math.rice.edu/~dfield/dfpp.html
Apr
15
comment Proof: The inverse of the translation $T_{AB}$ is the translation $T_{BA}$
The inverse of a function is the unique function which "reverses" the map, so $(T_{AB})^{-1}$ is the function such that for every $P$, $(T_{AB})^{-1} (T_{AB}(P)) = P$. You should be able to use that property to get what you want.
Apr
15
comment Proof: The inverse of the translation $T_{AB}$ is the translation $T_{BA}$
You are trying to show that $(T_{AB})^{-1} = T_{BA}$, so for any $P$ you need $(T_{AB})^{-1}(P) = T_{BA}(P)$.
Apr
6
comment $T$ is diagonalizable if $T^n$ is identity for some $n$
You are probably right.
Mar
20
awarded  Pundit
Mar
18
comment How do you calculate a fee percentage to handle a fee being charged?
I do not think it is fully clear what you are asking. Who is charging who? If you pay them 10.30, why are they paying you back?
Mar
14
comment Column Space and SVD
If $A = BC$, then the column space of $A$ must be a subset of the column space of $B$, since the matrix $BC$ is literally a matrix whose columns are some linear combinations of the columns of $B$. If $C$ is also invertible, then also $AC^{-1} = B$, which implies the column space of $B$ is a subset of the column space of $A$. Thus both inclusions hold so they have equal column space. Now set $B = US$ and $C = V'$.
Mar
3
comment What's the advantage of using a connection instead of embedding it to Euclidean space?
Ah, sorry. Well, in that case, it does seem possible to do as he proposes, only that construction of explicit embeddings does not seem trivial...
Mar
2
comment What's the advantage of using a connection instead of embedding it to Euclidean space?
For the case of the sphere, you are right that there is very little need for the full-fledged tools of differential geometry. But this is because the sphere can be entirely covered (excluding one point) by a single chart. But there may be manifolds where charts are "very local" so to speak, so that mapping to a Euclidean space is only "locally useful".
Feb
27
answered The difference between mathematics and statistics?