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

1
vote
1answer
63 views

What will happen if we try to reconstruct signal using phase only or magnitude only?

I am studying Fourier Transform and it's inverse. We get phase and magnitude from Fourier transform and reconstruct it back from both together My question is that What will happen if we try ...
1
vote
1answer
30 views

Eigenvectors and geometrical transformation

$$A= \begin{pmatrix} 2/3 & 2/3 & -1/3 \\ 2/3 & -1/3 & 2/3 \\ -1/3 & 2/3 & 2/3 \\ \end{pmatrix}$$, I need to understand that kind of ...
2
votes
1answer
39 views

The curvatures of a transformed surface under a similarity transformation

Setup: Let $f:\mathbb R^3\to\mathbb R^3$ be a similarity transformation. Then $f=rA+b$ for some fixed orthogonal matrix $A$, vector $b$ and nonzero real $r$. Suppose $S$ is a surface, and $S'=f(S)$. ...
2
votes
1answer
60 views

What is this subclass of the class of monotonic transformations?

Let $u$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$. Then $v$ is called a positive monotonic transformation of $u$ if $u(x) < u(y)$ if and only if $v(x)<v(y)$ and similarly for ...
2
votes
0answers
42 views

The Adrian Transformation of a function in $\mathbb{R}^{2}$

Recently I came upon a problem (if you would call it that, more of a thought experiment), which was phrased something like this: Rotate the area formed by $\int_{-1}^12dx$ around the curve ...
1
vote
0answers
51 views

Is this chain of inequalities correct?

Is this chain of inequalities correct? If not how to make it works? $$\frac{\ln \left( 1+x^3+y^3 \right)}{\sqrt{x^2+y^2}} \le \frac{\left( x^3+y^3 \right)}{\sqrt{x^2+y^2}} \le \frac{ \left( ...
0
votes
1answer
41 views

How to prove $\sqrt{Y}$ can be variance stabilizing transformation of poisson distribution?

I am studying constant variance checking when conducting ANOVA. I know that $\sqrt{Y}$ is one of the common transformations for a Poisson distribution, but I can't prove it. I also read Anscombe ...
2
votes
1answer
33 views

Identifying translations and rotations as compositions.

I am having trouble understanding the below which are the ones underline in red and blue. For the red: Why is that $R_{A,90}(A)=A$ and that $\tau_{AB}(A)=B$ As for the blue: Why is that ...
0
votes
0answers
15 views

What is or how do you get the rotational matrix of 4-D vector onto the xyz-space?

which would make the 4-D component 0. To be honest I'm not really sure how 4-D rotations work. I know about the simple rotations but not the mechanism in how it rotates, and I'm not sure whether to ...
1
vote
1answer
26 views

Does the following series of transformations of inequalities holds?

I am to calculate limit of the function $f(x,y)$ i am trying to apply squeeze theorem. Is the following series of transformations of this inequality correct? If not how to do this correctly? i.e. are ...
3
votes
1answer
25 views

Let $R$ be any rotation and $P$ any reflection then $R \circ P$ and $P \circ R$ are both glide reflections

Let $R$ be any rotation and $P$ any reflection then $R \circ P$ and $P \circ R$ are both glide reflections I am having trouble showing $P \circ R$ is a glide reflection, I manage to get $R \circ P$, ...
1
vote
0answers
41 views

Solids of Revolution around other functions.

Recently I've been thinking about solids of revlution, and thought about an interesting experiment. Can you rotate functions around, for example, the line $f(x)=x$? And consequently, could you rotate ...
0
votes
0answers
12 views

Transformation of graphs, finding the values of unknowns

I am a second grade IB student using "Mathematics Standard Level for the IB Diploma, Cambridge" book.This is the question I have a problem with: "Let f(x)=(3x-5):(x-2) a) Find the value of constants ...
0
votes
2answers
63 views

Find a basis for Kernel and Image of a Linear Transformation

Given: $$A = \left\{\begin{bmatrix} 0 & 1 \\ 0 & 2 \\ 0 & 1 \end{bmatrix}\right\}$$ Find a basis for $ImT_A$ and $kerT_A$ So far, I've ...
0
votes
1answer
33 views

generating system of the kernel of a module-transformation

Let $G ≠ 1$ be a group and A a commutative ring. Now, the group ring $A[G]$ is naturally an A-module. Next, let's consider the transformation: $$\phi: A[G] \to A, \sum_{g \in G} a_gg \mapsto \sum_{g ...
1
vote
0answers
52 views

How can I transform coordinate systems based on quaternion data?

I have a single rigid body object, and its orientations in quaternion with respect to two coordinate systems, each is called original and prime, respectively; therefore, I have two quaternions ...
1
vote
2answers
22 views

Why cannot the homogeneous coodinates be zero?

Given a point (x, y) on the Euclidean plane, for any non-zero real number Z, the triple (xZ, yZ, Z) is called a set of homogeneous coordinates for the point. Why can't Z be zero?
0
votes
1answer
66 views

How to transform function values to specific interval

I'm doing a project at university about scientific computing and I'm stuck. As in: I seem to lack quite a bit of mathematical background for this project. The program has as input an array of $x$ ...
0
votes
0answers
13 views

transformation of variables in Melnikov method

Supposing there is a system of non-autonomous non-linear differential equations with small damping and small forcing. The unperturbed system (zero damping and forcing) is Hamiltonian but neither has a ...
0
votes
1answer
28 views

Is the transformation $T: (r, \theta) \to (r, \theta + \phi)$ linear? Here $\phi$ is a given angle

Let $T$ rotate every point through the same angle $\phi$ about the origin, $i.e.$ $T: (r, \theta) \to (r, \theta + \phi)$ where $\phi$ is given. If in addition that $T(O) = O,$ namely, if $T$ maps the ...
1
vote
1answer
22 views

Terminology with linear transformation

I am working on a problem that asks me to "Write C for the matrix whose ij entry is $(1/2)^{ij}$" given that $M$ is the vector space of all $n x n$ matrices and $l$ is a linear transformation on $M$. ...
0
votes
0answers
60 views

How to wrap 2D image around a circular arc?

How to transform rectangular image to image that is bent at certain radius? On the plot the center line follows the radius which is 2. Conformal transformation would be this, but there should be ...
0
votes
0answers
19 views

Composite Transformation expressed as single transformation

Is this right following the composition rule. Also, i know that we can add or subtract 2 pie so as to make the number nicer, by adding 2 pie in the case i shouldn't be wrong right ?
1
vote
0answers
30 views

mobius transformation form $M= B(0,1)\setminus\overline{B(1,\sqrt2)}$ to a sector.

I know that the intersections of the two circles need to be sent to $0$ and $\infty$ in order to get a sector $S = \{x+iy: x>0,0<y<x\}$ The intersections of the two balls were i and -i. So i ...
2
votes
0answers
36 views

The Composition of Two rotations

So far I rewrote the halfturns of d,c,b,a to halfturn (p,n)(m,l) where n=m because lines c and d are parallel so I can make ambiguous lines n and p parallel too. I also know that lines c,d can be ...
1
vote
0answers
42 views

Transformation that f(A+B)=f(A)+f(B) and f(AB) = f(A)f(B)

if $f:M_{n*n}(F) \rightarrow M_{m*m}(F) $ and f transformation identity to identity matrix and $f(AB) = f(A)f(B) , f(A+B)=f(A)+f(B)$. now we want to prove there is an integer like $k$ that $m = k*n$
0
votes
1answer
28 views

How principal component analysis ensures component orthogonality when using zero co-variance as the restriction to maximize variance?

I am currently learning the mathematics behind PCA and I found when PCA maximizes variance to find out the 2nd, 3rd, ... components, it uses zero co-variance as the restriction, as shown below, ...
4
votes
3answers
268 views

Transforming a function by a sequence geometric operations on its graph.

I am solving the following problem: Let $f(x) =\sqrt{x}$. Find a formula for a function $g$ whose graph is obtained from $f$ from the given sequence of transformations: shift right $3$ ...
0
votes
1answer
35 views

Find the image of the unit vector at the point $z_0=i$ under the function $f(z)=z^2+2z$

From this image find the rotation angle and the expansion factor. $z\in\Bbb C$ I am unsure how to find a way to accurately plot the image. I understand that the image should expand because the ...
4
votes
3answers
66 views

Prove that the map $f(z)=\frac{1}{z}$ sends any line onto either a line or a circle.

Show the cases in which the image is a line and the case in which the image is a circle. I understand that representing the equation of line, ($ax+by+c=0$ $a,b,c\in\Bbb R$ $a,b\neq0$ at the same ...
1
vote
1answer
36 views

Is centre of a circle remains invarient under Movius transformation?

Prove that the image of the center of a given circle is never the same as that of the circle image under a linear fractional map. Given some linear fractional map$f(z)=\frac{az+b}{cz+d}$, that is ...
1
vote
1answer
30 views

Linear Transformations

I have no idea how to work this question. Can someone offer some insight?
3
votes
2answers
49 views

How does $y=|x+3|+4$ become $y=\frac{1}{2}|2x+3|+4$ (compositions and translations)

Today, I had a test question that was bothering me because my friend and I had different answers to it. It's a grade 12 math question. It's telling us to explain the changes that were made to the ...
0
votes
4answers
98 views

Eigenvalues and Eigenspaces of a Projection

Let $P$ be the orthogonal projection onto a subspace $E \subset V$ ($V$ being an inner product space) with $\mathrm{dim(V)}=n$, $\mathrm{dim(E)}=r$. Obtain the eigenvalues and eigenspaces, along with ...
1
vote
2answers
46 views

Transformation of xy plane to polar coordinates. (What would be the bound of polar coordinate?)

I have a double integral $$\int_0^a \int_0^x (x^2+y^2)^{1/2} \operatorname d y \operatorname d x$$ So, I am double-integrating $r^2$ What would be the region of the polar coordinate..?
0
votes
1answer
41 views

Stereographic Projection from an Arbitrary Point

Let $p \in \mathbb{S}^{n}$, then the stereogaphic projection is a diffeomorpshim $h:\mathbb{S}^{n} \setminus \{p\} \to \mathbb{R}^{n-1}$. Suppose that $p$ is the 'north pole' ($p = (0,0,..,1)$), then ...
0
votes
1answer
33 views

Why is this laplace identity true $\int_{\Bbb{R}^+}\frac{f(t)}{t}\,dt = \int_{\Bbb{R}^+}\mathcal{L}\{f\}$?

I was wondering why this laplace identity is true? Does it follow from definition? $$\int_{\Bbb{R}^+}\frac{f(t)}{t}\,dt = \int_{\Bbb{R}^+}\mathcal{L}\{f\}$$ I'm trying to understand the first ...
2
votes
1answer
52 views

The Matrix of a Transformation from P2 to P1

I don't understand how T(1), T(x), and T(x^2) were found in the picture so I did it using another method I saw on StackExchange. (a + b)x - c => -c + (a + b)x + 0x^2 so the first row would be {0, 0, ...
0
votes
1answer
45 views

Line plane intersection

I have two planes in $\mathbb R^3$ as shown below: axes representation corrected after MvG's comment Each plane is a finite area, a rectangle with length and width $H_l, H_w$. Each plane has its ...
1
vote
0answers
33 views

inverse laplace tranform

I have a simple question, There are some functions f(t), g(t) and lets say F(s) and G(s) for the form of Laplace transform of f(t) and g(t), respectively. While I am solving differential equation ...
1
vote
0answers
60 views

How do I calculate 3D movement based on yaw, pitch and roll?

I'm creating a 3D game demo and I need to calculate the position of the player in the space (i.e. the player's x, y and z coordinates). I understand that this would be affected based on the camera ...
0
votes
1answer
21 views

Is a series that contains the index term a function of the same series without the index term?

Can it be shown that $U_{2} = \sum_{i=1}^{n} [i*g(Y_{i})]$ is a function of $U_{1}=\sum_{i=1}^{n} g(Y_{i})$ ? My intuition tells me that this is not true because of the changing (for lack of a ...
0
votes
0answers
15 views

changing variables and taking limits respectively

Say we have the equation $3\left[a\frac{d}{dx}+R\right]\frac{\alpha^{4}}{R^{2}}=R$ If we make the trasformation $\phi=\frac{\gamma}{R}$ and $a\rightarrow{a_{0}+\gamma{a_{1}}}$, where ...
4
votes
2answers
68 views

Fractional Linear Transformation: Region between two circles to strip

I'm trying to find Fractional Linear Transformation (if one exists) that maps the region between the circles $\|z+1| = 1\}$ and $\{|z|=2\}$ to the region between the horizontal lines $Im(z) = 1$ and ...
1
vote
1answer
43 views

Prove the result of multiplying a complex number by (1 + i)

I know that if I multiply a complex number that has the form a + bi by the number (1 + i), this will rotate the vector that corresponds to the complex number by 45 degrees in the counterclockwise ...
1
vote
0answers
42 views

Reducing heat equation into nondimensional form

I want to get nondimensional form of heat equation $u_t=a(x,t)u_{xx}$. For the case of $a(x,t)=a(t)$, by setting $A(t)=\int_0^ta(\eta)d\eta$ and $t=\phi(\tau)$, where $\phi$ is the inverse mapping ...
0
votes
0answers
17 views

Make a conform map g that sends the unit disk to $A = \{w: \operatorname{arg}(w) \in(\frac{\pi}{4},\frac{3\pi}{4})\}$ such that $g(2i) = 0$

make a conform transformation g that sends the unit disk to $A = \{w: \operatorname{arg}(w) \in(\frac{\pi}{4},\frac{3\pi}{4})\}$ such that $g(2i)$. I actually solved it by taking the inverse of $f(x) ...
1
vote
0answers
100 views

Mapping A point from one 3D Coordinate System to Another 3D coordinate System with Euler Angles between the two systems given

Suppose I have a point in the green coordinate system, and I wish to describe it in reference to the orange coordinate system. I know the roll, pitch, and yaw of the green system with respect to the ...
0
votes
0answers
5 views

How to take dft of irregularly sampled function in k space?

I would like to take inverse dft of irregularly sampled complex function in k-space. I am just summing in a loop over the length of the k vector, but is quite slow. ...
0
votes
0answers
20 views

how can I find matrix of linear transformation for this specific problem

I am migrating my problem here with the hope of getting some assistance http://stackoverflow.com/questions/29029523/how-do-i-find-the-matrix-of-the-linear-transformation