# Tagged Questions

Transformation has many meanings in mathematics. If using this tag, add another tag related to the object being transformed. If there is a tag for your specific kind of transformations, use that one instead: e.g., (laplace-transform), (fourier-analysis), (z-transform), (integral-transforms), (rigid-...

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### Relative Motion between two rotating frames

I am looking for mathematical relations between equations of motion between two rotating frames. Relating the said motion by first going to a globally fixed frame is not an issue but how to approach ...
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### Scale a rectangle about a point considering reflection

Given a rectangle of width $(w_0)$, height $(h_0)$, left $(x_0)$, top $(y_0)$. How do I scale it from an origin $(x_1,y_1)$ with a scale factor of $(w_1, h_1)$ taking into account reflection? This ...
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### Understanding bounded linear operators

The definition of a bounded linear operator is a linear transformation $T$ between two normed vectors spaces $X$ and $Y$ such that the ratio of the norm of $T(v)$ to that of $v$ is bounded by the same ...
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### Certain symmetrized product of cosines - can it be transformed into more manageable form

I am interested in the following expression: $$F_{k_1,\ldots,k_n}(t):=\sum_{\sigma\in S_n}\cos(\sigma(1)k_1t)\cos(\sigma(2)k_2t)\cdots\cos(\sigma(n)k_nt)$$ where $k_1, \ldots, k_n$ are natural ...
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### Find equation of log function given graph

How would you find the equation of this log graph with respect to transformation of the function $$a\log[k(x-d)] + c$$ I had trouble solving this accurately.
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### Fast procedure to know which transformations are linear

I have the following transformations: How can I tell if the transformation is linear? Is there a fast way of knowing (by looking at equations)? or do I need to check through the theorems: ...
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### Group of Motions

In Needham's Visual Complex Analysis on pdf page 57, book page 37, Needham says that the set of indirect/opposite motions (motions reflecting the angle of a vector input) does not form a subgroup of ...
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### Finding a transformation that yields a prescribed PDF

I am attempted to procure a function from a composition when given the PDF (I typed the full problem at the bottom in its entirety in case I left out details in my inquiry). I understand how to get ...
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### Find and sketch the image of the straight line $z = (1+ia)t+ib$ under the map $w=e^{z}$

I need to find and sketch the image of the straight line $z = (1+ia)t +aib$, where $-\infty < t < + \infty$, $a,b\in \mathbb{R}$, and $a \neq 0$, under the map $w = e^{z}$. In order to ...
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### Inverse Fourier transform of $\frac{\alpha}{\alpha+\|w\|_2^d}$

I want to calculate the inverse Fourier transform of $\frac{\alpha}{\alpha+\|w\|_2^d}$ where, $w \in R^D$ and $d$ is some positive integer. $\| \|_2$ is a 2 norm of a vector and $\alpha$ is some ...
### optimal monotonic transform: $\min_f (f(x)-y)^2$
Given two vectors of length $N$ denoted by $x_i$ and $y_i$, $1\leq i\leq N$, what is the monotonic transformation $f(x)$ that minimizes the overall distance $D=\sum_{i=1}^{N}{(f(x_i) - y_i)^2}$. Does ...