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), ...

learn more… | top users | synonyms

0
votes
0answers
14 views

Real Linear vs. Complex Linear

I recently started a new math course and got hung up on a particular problem from the book "Linear Algebra Done Wrong". Specifically, problem 1.3.6 (c). I am an engineer, and I believe I simply lack ...
0
votes
1answer
24 views

What should I do to tackle the following matrices calculation?

Through chapter 3 of Group Theory by Morton Hamermesh in part 3-6 (Equivalent representations; characters.) I stopped in some point. It's told "If we change the basis in the n-dimensional space $L$, ...
-1
votes
0answers
12 views

Fourier sine and cosine transform [on hold]

Why e raise to power x is not defined for Fourier sine and cosine transform I read in some book that it is not defined for bounded region. But I could not understand the logic behind it.
2
votes
1answer
29 views

How to understand the Mobius transform as a group action?

The group $SL(2,R)$ acts on the upper half-plane by the formula $$ \left(\begin{array}{cc} a & b \\ c & d \end{array} \right) z = \frac{az + b}{cz + d} .$$ It is indeed straightforward to ...
0
votes
0answers
4 views

Using Jacobi eigenvalue decomposition for decomposition into non-eigenvalue matrix?

I am a student in computer vision struggling with the problem of camera calibration. I am having trouble decomposing a matrix, Q, according to the formula: ...
0
votes
2answers
51 views

Non linear map that accomplishes $f(v+u) = f(v) + f(u)$

Can someone give an example of a non linear map, $f: V \to V$ that accomplishes $f(v+u) = f(v) + f(u)$ for all $v$, $u$ in $V$, but does not accomplish $k f(v) = f(kv)$ for some $k$ in $K$? ($V$ is a ...
0
votes
0answers
12 views

Coordinate transformation, specific expression

This is a fairly specific question, on which I'm stuck while reading a paper. If someone could enlighten me, thanks in advance! We have a function F(l), a Fourier transform of some function f(x). ...
0
votes
1answer
16 views

is the diagonalization of a matrix a linear transformation?if yes, then how

How diagonalization of a matrix can be called as a linear transformation? Since multiplying a matrix A by P(inv)AP is not a linear operation
1
vote
1answer
16 views

About the stable/invariant point sets in a plane with respect to shift/linear transformation

I'm reading Vlademir A. Zorich's Mathmatical Analysis I, meeting exercise question as following: a) A set $S \subset X$ is stable with respect to a mapping $f:X \rightarrow X$ if $f(S) \subset ...
1
vote
1answer
21 views

Fourier expansion and transform - what about the phase of the waves that i am adding?

Say we have a wave on the surface of the water and we want to describe it as a sum of other waves. So we use Fourier expansion to add waves of different wavelengths. For simplicity, say we have to ...
2
votes
1answer
24 views

Polynomial Transformation

In the AOPS vol 2 problem solving book, it states that you can find the sum of the reciprocals of a polynomial by flipping the coefficients(first -> last, last -> first etc). The book summarized the ...
1
vote
0answers
27 views

Show that boundary layers diffuse out from the plate with speed $\sqrt{\frac{\nu}{t}}$

I was wondering if somebody would be able to help me with this problem. I know how to solve it using dimension arguments but I'm unsure what is meant by 'transform techniques'. Any help would be ...
-2
votes
0answers
19 views

How to transform 3 probability values to a specific range?

There are 3 probabilities say x, y and z such that x+y+z = 1. Now, we need to convert these three probabilities together in the range of 0 to 1. If x is 1 then it should be 0, if y is 1 then it should ...
1
vote
1answer
14 views

Linear transformation with matrices in base

Consider the vector space of real $2 x 2$ matrices and take as base $\{{E_{11},E_{12},E_{21},E_{22}}\}$. Where $E_{ij}$ represents the matrix with a $1$ in the $i$-th row and $j$-th column and the ...
-1
votes
1answer
37 views

Linear transformation that must not be an isomorphism

I am a bit lost on this one: Let $a$ and $b$ be linearly independent vectors and $T: \mathbb{R}^3\to\mathbb{R}^3$ the transformation given by the rule: $$T(x)=x-(b\cdot x)a,$$ where $b\cdot x$ is ...
0
votes
0answers
20 views

Scaling Matrix?

I have two matrix problems which I have no idea of how to start solving. If possible could someone guide me through this? Links to videos would be great so I can solve future problems myself 1) Find ...
1
vote
0answers
32 views

Fourier transform of the Cosine function with Phase Shift?

How can i calculate the Fourier transform of a delayed cosine? I haven't found anywhere how to do that. This is my attempt in hoping for a way to find it without using the definition: $$ x(t) = ...
1
vote
0answers
8 views

Request reflection matrix about these types

Supposed there's $(a,b)$ point and going to be reflected and find the mapping. The baseline formula will I use is $\begin{pmatrix} x' \\ y' \end{pmatrix}=M_{R} \begin{pmatrix} x \\ y \end{pmatrix}$. ...
0
votes
2answers
29 views
+50

Single transformation matrix of $A \circ B$ and $B \circ A$ with certain conditions

Let $A$ is 2x1 translation matrix and $B$ is 2x2 matrix of reflection or rotation matrix (reflection, rotation, etc.). Suppose I want to find the mapping of a $y=mx+c$ line and the mapping is done by ...
0
votes
1answer
16 views

Transformation of general equation of second degree with respect to a rectangular axes

Question : The equation $3x^2+2xy+3y^2-18x-22y+50=0$ is transformed to $4x^2+2y^2=1$ with respect to a rectangular axes through the point $(2,3)$ inclined to the original axes at an angle $\theta$. ...
1
vote
3answers
49 views

How is that a rotation by an angle θ about the origin can be represented by this transformation matrix?

$$ \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix} $$ How was this matrix derived? I know how to use it, but where did it come from? Can someone prove why ...
0
votes
2answers
31 views

How to do Fourier transform for these 2 questions?

I don't get certain of parts of these two questions 1) I'm trying to do the Fourier transform of: $$f(x) = \, xe^{-x^2} $$ In the problem it said to use: $$F \, (e^{-tx^2}) = ...
0
votes
0answers
8 views

3D point rotation round a fix reference point

I want to compute a transformation from 3D point A to 3D point B through a reference point 0 which is fixed. I have the 6DOF transformation from A - 0 and B - 0. That is x,y,z and Quaternions of ...
0
votes
1answer
22 views

Equation of the plane tangent to the given surface

Find the equation of a plane tangent to the surface given by $$xyz+x^2-3y^2+z^3=14$$ at $$P=\left( 5,-2,3 \right)$$ In my opinion answer is: $$4x+27y+25z-41=0$$ If not please tell me what am i doing ...
1
vote
1answer
18 views

Transform to flatten a parametric curve (polynomial)

Given a polynomial parametrized by $p(t)=(x(t),y(t))$ such that $y(t)=p(t)$, $x(t)=t$, and $p(t)= \sum_{i=0}^na_it^i$, for real coefficients $a_i$, is there some transformation I can take such that ...
0
votes
0answers
5 views

Local point axis, orthogonalize, re-calculate spaces for faces of objects

I have a problem, I have 2 different facing objects, I want to move them in space to same. I have for this reference point at rp[0,0,0] . Idea is that I will choose 1 point as centre call it [c], make ...
0
votes
0answers
5 views

How to match the time for given points in two different 3D Cartesian coordinate system?

I have two machine to record a men's motion (what we actually record are the 3D coordinates of the men's 14 different body parts). machine 1 record the coordinates 100 times per second, and machine 2 ...
0
votes
1answer
20 views

Find diffeomorphism transforming the following areas:

Find diffeomorphism transforming the following: interior of the triangle T with vertices in $(0,0),(0,1),(1,0)$ onto the interior of the circle of radius 1 and centre in $(0,0)$. Obviously i am ...
1
vote
1answer
33 views

Transforming a sequence to distinguish a limit

This might be the wrong place to ask this question, but I figured I might get some creative answers: I have a decreasing sequence $\{a_n\}_{n \geq 1}$ with $a_k \in (0,1)$ for all $k$ and $a_n \to ...
1
vote
1answer
32 views

Is there a difference between cosine and sine transform?

Surely both should work with the same set of functions. Why is only cosine transform used in JPEG? Why not sine? It seems that using fourier transform rather than cosine transform would result in ...
0
votes
0answers
18 views

Motion estimation of a rectangle on a planar surface

(Significantly edited following the comments) I have 4 points (x,y) forming a rectangle on a plane, and this rectangle moves around the plane (the shape of the rectangle remains the same). With the ...
0
votes
1answer
12 views

Offsetting a 2-D polynomial

I have a surface that is defined using a two dimensional polynomial: $$z = f(x) + g(y)$$ I want to offset the curve in the $XY$ plane from a point on the surface $\left(x_0, y_0, z_0\right)$ to a ...
1
vote
0answers
34 views

(Numerical) Integration in log space

I have some function $f(x)$, which I'd like to integrate to find, $F(r) = \int_r^\infty f(x) dx $. Is there a way to do this using the values parametrized in log-space? I.e. some function $G(r, ...
4
votes
1answer
45 views

Generalising Plane Isometries to $\mathbb{R}^3$

Firstly, I DO NOT WANT PROOFS OF ANY OF THESE THEOREMS, as I wish to prove them myself. However, I would like to know the correct generalizations to $\mathbb{R}^3$ of the following theorems: An ...
1
vote
0answers
29 views

Why $\lim_{a\to\infty} \frac{ Q_0(a,b)}{ \sqrt{a e}}e^{\frac{(a-1)^2}{2}}\neq Q (b)$?

I’m trying to find a connection between Marcum-Q function, which is defined as: $$Q_M(a,b)=a^{1-M}e^{-\frac{a^2}{2}}\int_{b}^{\infty} x^M \exp^{-\frac{x^2}{2}} \mathrm I_{M-1}(a x)\mathrm dx$$ where ...
1
vote
2answers
61 views

What amplification can I apply to $y=\sin x$ for it to be a perfect oscillating arc?

A perfect arc is $y=\sqrt{|1-(x-1)^2|}$. A sin wave is $y=\sin({\pi x\over2})$ I am curious how I can amplify the sin wave so that it's a perfect alternating arc. In the link below you can see ...
1
vote
1answer
68 views

$\mathbb{R}^3 \to \mathbb{R}^3$ transformation: reflection across a plane

Notation: $v$// is $v$ parallel symbol, $v\bot$ is $v$ perpendicular, and both are relative to plane $\sqcap$ Let $\sqcap \subseteq$ $\mathbb{R}^3$ be the plane whose equation is $x + y + z = 0$. ...
0
votes
0answers
10 views

Pseudo-log transformation returning positive values

I'm looking for a transformation that acts similarly to natural log, but I want to return positive values only. My untransformed values range from 0.01 to 50. Of course I could simply offset the log ...
0
votes
0answers
7 views

How can I do a longitude/latitude tilt transformation?

I am trying to find a way to express the shortest path between two random points on a globe as a function expressed in longitude/latitude without using the geodesic equation (because it's messy and I ...
1
vote
1answer
83 views

Isolate $z$ in equation

This is an equation to find the field strength of a cylindrical magnet at a given distance. I'd like to reverse it and find a distance for a given field strength along the polar axis. z is length D ...
0
votes
2answers
40 views

What is the motivation behind this (tested, working) 2d coordinate transform?

I am working with programming and 2d geometry and need to transform between two different coordinate systems. I have two different representations of the same world, where I can sample any point and ...
1
vote
1answer
26 views

why should add one column using Moore-Penrose pseudoinverse

I have a code from someone that I dont understand: This code is written in matlab and the function is to estimate linear geometric transformation [1] of a matrix using pinv. The size of first matrix ...
1
vote
1answer
26 views

Combining Moebius transformations

Moebius transformation in this case $\frac{az+b}{cz+d}$ for complex $z$. I have several transformations I want to apply to an initial $z$. For example first transform $f(a,b,z) = z + (a + bi) = ...
0
votes
1answer
27 views

Linear, Squared and Logarithmic scales with given input domain and output range

The input domain is $[12,24]$ and the output range is $[0,720]$. Now I know that with using linear scaling the value $16$ of the input range is mapped to $240$; with using sqrt scaling the same value ...
0
votes
0answers
29 views

Rotating one coordinate system about another

I have two coordinate systems: A and B. I also have a point p, whose position relative to ...
1
vote
1answer
22 views

Simplifying transfer functions in Z domain

I have difficulties to check whether the below transfer function is recursive or non-recursive: $$H(z)=\frac{1-z^{-1}+z^{-2}-3z^{-3}}{z^{-2}(1-z^{-1})}$$ I know that I have to multiply the num and ...
0
votes
1answer
55 views

Given a transformation, find the generating function

There's a mapping $(x,y) \mapsto(u,v)$ given by $u= x\cos\theta-y\sin\theta$ $v =x\sin\theta + y\cos\theta$ I'd like to find a generating function $G(x,y)$ for this mapping, which I understand to ...
1
vote
0answers
18 views

Determine mutual location of two coordinate systems, given two sets of points

My problem is: we've got tracking device and a robot. Tracking device provides set of $n$ points in cartesian coordinates(taken from marker on robot arm) and robot driver returns position of TCP(tool ...
0
votes
0answers
4 views

Transformation from unknown orientation representation to DCM

I'm working with some really strange software which has some sort of custom orientation representation, and I'm trying to get it into a standardized format (direction cosine matrix). However, that's ...
0
votes
0answers
79 views

Is there a space in which the $\vec a$ in $\sin(a_1\cdot x)+\sin(a_2\cdot x)$ is linear?

I have equations of the form $\sin(a_1\cdot x)+\sin(a_2\cdot x)=y$ (actually more complicated, but that's the general essence). I want to solve for $\vec a$ using linear regression instead of ...