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), ...

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3
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1answer
38 views

Are $B=PAP^{-1}$ and $B=P^{-1}AP$ equivalent?

Im looking at the solution to one of my questions. Basically, we started off with a matrix $A$ (in the elementary basis) which we want to convert into a diagonal matrix $B$ of another basis. Question ...
0
votes
2answers
43 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 ...
2
votes
2answers
726 views

Approximate a polynomial function using a sum of sine waves

I have a polynomial function which I need to approximate by a sum of sine waves with constant amplitude along a given domain. From what I hear, this might be a good time to make use of Fourier ...
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 $L$, ...
3
votes
2answers
3k views

building transformation matrix from spherical to cartesian coordinate system

How to arrive at the following from given $ x = r\sin \theta \cos \phi, y = r\sin \theta \sin \phi, z=r\cos\theta $ $$ \begin{bmatrix} A_x\\ A_y\\ A_z \end{bmatrix} = \begin{bmatrix} \sin ...
-1
votes
0answers
13 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.
1
vote
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 ...
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 ...
0
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1answer
339 views

How can I transform a 3D triangle to xy plane

Suppose I am given a triangle ABC and its corresponding vertex coordinates in 3D. I want to transform ABC in such a way so that vertex A lies on global (0,0,0) coordinate, B lies on (dist, 0, 0) ...
0
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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
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). ...
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votes
2answers
30 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
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
2answers
85 views

How can I calculate the origin of a scale transformation, given the starting and ending coords and dimensions?

Background: I have two sets of coordinates/dimensions. One for the red rectangle and one for the blue rectangle, as shown below. The blue rectangle is quite simply the red rectangle transformed by ...
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
22 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 ...
1
vote
1answer
443 views
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 ...
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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 ...
0
votes
1answer
134 views

What happens to Fourier Transform of function when the function's time scale is changed?

When a function $f(t)=exp(-|t|)$ for example undergoes Fourier Transformation, it gives $F(w)=\frac{-2}{1+w^2}$ But what happens to the result if the time scale is scaled and shifted, so that $t ...
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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) = ...
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
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 ...
1
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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
1answer
17 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
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
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1answer
2k views

Negative & Positive Shear Factor

My question relates to constructional geometry & matrices aren't to be involved in the solution because stated Math level is up to O Levels... The figure below shows shear with y=3 as invariant ...
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
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
1answer
755 views

Finding reflection of a matrix

To 2 decimal places, what is the value of the lower-right entry in the reflection matrix $Q_a $if a = 1.05? Not even sure where to begin, is there a formula? This is what I could find in my textbook ...
1
vote
3answers
31 views

Composition of Rotation and Translation in the Complex Plane — Finding Angle of Rotation and Point

A rotation about the point $1-4i$ is $-30$ degrees followed by a translation by the vector $5+i$. The result is a rotation about a point by some angle. Find them. Using the formula for a rotation in ...
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 ...
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
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 ...
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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, ...
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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
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 $x + y + z = 0$. ...
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
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 ...