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
1answer
178 views

Transformation Matrices [duplicate]

Possible Duplicate: Why can any affine transformaton be constructed from a sequence of rotations, translations, and scalings? Assuming that I have a set of points in a co-ordinate system (I ...
4
votes
1answer
3k views

Matrix for rotation around a vector

I'm trying to figure out the general form for the matrix (let's say in $\mathbb R^3$ for simplicity) of a rotation of $\theta$ around an arbitrary vector $v$ passing through the origin (look towards ...
0
votes
1answer
211 views

Prove equivalency of orthogonal transformation, $h(f(x),f(y))=h(x,y)$ and $f$ maps an orthonormal basis to another?

Please help! How do I go about proving this please? Let $f: M \longrightarrow M$ be a linear transformation. Then the following are equivalent: a) $f$ is an orthogonal transformation. b) ...
6
votes
1answer
1k views

How to figure of the Laplace transform for $\log x$?

I was looking at a table of common Laplace transforms of functions when I came across the transform for $\log x$. Apparently, the transform is as follows: $$\mathcal{L} \left\{ \log ...
2
votes
1answer
86 views

Change of coordinate codomain from $[-1,1]$ to $[0,1]$

How does one translate coordinates from $[-1,1]$ to $[0,1]$? That is, suppose we have an ordered pair $(x,y)$ which lies between $[-1,1]$ and want to push into the range delimited by $[0,1]$. A lot ...
0
votes
2answers
72 views

Normalize $X$ to $0$ to $10$ scale with asymptotes at either end

I am trying to find a scaling function that mimics the gas gauge in a car. I would like to map a value to a $0$ to $10$ scale, on which I have two known points. For example: $X_1 = 2$, $Y_1 = 2.5$, ...
1
vote
1answer
277 views

What do the parameters skewX and skewY mean in the transform specified by Flash's motion XML?

Flash has the ability to export animations into a format they call motion XML. Its specification is here I am trying to write a python renderer for these animations using pyglet. I understand ...
0
votes
1answer
361 views

Affine transformation matrixes

I could use some advise with the following problem: Lets say there is a cuboid that has two distinguished points - that is one of its vertexes ($A$) and the other one is somewhere on the surface ...
1
vote
0answers
573 views

2D Projective transform

Let's say we're transforming a square to an arbitrary 4 points via projective transform. Is there a way to ensure that the resulting points have homogeneous coordinates that are >0 ? i.e. sending ...
1
vote
1answer
715 views

rotating a rectangle via a rotation matrix

I want to rotate a 2D rectangle using a rotation matrix. After the rotation, I want the points (x, y) of the rectangle to be: ...
1
vote
0answers
368 views

How to project a spherical map onto a sphere / cube

I have this panorama, an spherical map from google streetview, and want to map this on a sphere/cube. Below are some examples and illustrations, i am going to implement it in c++ and are not sure ...
1
vote
2answers
5k views

How can I construct the matrix representing a linear transformation of a 2x2 matrix to its transpose with respect to a given set of bases?

I have been given that I am working with the space of all 2x2 matrices. The basis $B$ for this space is given as a set of four 2x2 matrices, each with an entry of 1 in a unique position and zeroes ...
0
votes
1answer
708 views

Finding the transformation matrix to transform one triangle into another

I have 2 sets of 3 points: the "origin" and "destiny". Any ideas on how to find the best-fit transformation matrix that will convert the origin's points to destiny using (only) rotation, scaling and ...
11
votes
2answers
1k views

Is a Fourier transform a change of basis, or is it a linear transformation?

I've frequently heard that a Fourier transform is "just a change of basis". However, I'm not sure whether that's correct, in terms of the terminology of "change of basis" versus "transformation" in ...
2
votes
1answer
116 views

How can I determinate the bases for the most simple representation of a linear transformation?

Imagine a linear transformation $\Phi : \mathbb{R}^4 \rightarrow \mathbb{R}^3$ with the ordered standard basis: $B = (\begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 ...
0
votes
1answer
100 views

General transformation matrix

I am currently working through some of my maths assignment, and i have this question, and i can't work out what it means, and i am sure there is something to missing which would make this question ...
0
votes
1answer
204 views

Need a transformation matrix to convert to new base vectors

I was searching for a solution, but can't find anything I can use with my superficial knowledge. So, I have vector A, vector B & vector C. I want to convert the space to base vectors A & B ...
0
votes
1answer
433 views

Plane transformation

I have a plane-A which sits on the origin and where every point on the plane has a z coordinate of 0 (so there is no rotation of the plane). I have plane-B in space and I have a a point (which is the ...
1
vote
1answer
638 views

Find 3D rotation vector and angle to transform a rectangle into a given quadrilateral

I have a given rectangle that I need to transform into a given quadrilateral shape that resulted from a rotation and translation in 3D space, and subsequent projection. ...
10
votes
3answers
5k views

Get Transformation Matrix from Points

I have built a little C# application that allows visualization of perpective transformations with a matrix, in 2D XYW space. Now I would like to be able to calculate the matrix from the four corners ...
2
votes
1answer
2k views

How to find the orthonormal transformation that will rotate a vector to the x axis?

I am having trouble remembering linear algebra. I need to find the orthonormal transformation that will rotate a 3-dimensional vector to the x axis. I could not find any similar question on the net. ...
1
vote
2answers
3k views

How can I determine the scale factor of a pantograph from the ratio of the arms?

I know this is probably simple but I just can't see it. How can I determine the scale factor of a pantograph from the ratio of the arms?
1
vote
1answer
408 views

What is the relation between complex numbers and transformation matrices?

I read addition and multiplication with complex numbers can be represented as translation and rotation in a 2D plane. I am using this to move around objects on the screen. I have an offset number, ...
1
vote
1answer
311 views

Is a linear conformal mapping same as a similarity transformation?

For a mapping between two Euclidean spaces, is it a linear conformal mapping if and only if it is a similarity transformation? My answer is yes, because the Jacobian matrix of a conformal ...
1
vote
0answers
314 views

Fast Walsh–Hadamard transform generalization for non-power-of-two orders?

I have to process vectors through a Hadamard matrix of order N. If N is a power of 2, I can use the Fast Walsh–Hadamard transform; but if N is not a power of two (for instance, N=12), it is not ...
0
votes
1answer
215 views

Finding the transformation matrix when transformations are given…

Question: For set of vectors {$x_1,x_2$}, $x_1=(1,3)^T, x_2=(4,6)^T$ are in $R^2$. Find the matrix of linear transformation $T:R^2\rightarrow R^3$ such that $Tx_1=(-2,2,-7)^T$ and $Tx_2=(-2,-4,-10)^T$ ...
6
votes
3answers
2k views

Is it true that any matrix can be decomposed into product of rotation,reflection,shear,scaling and projection matrices?

It seems to me that any linear transformation in $R^{n\times m}$ is just a series of applications of rotation(actually i think any rotation can be achieved by applying two reflections, but not sure), ...
1
vote
2answers
743 views

How do I map the torus to a plane?

Please see my answer on Perlin noise first. A bit of background. Imagine a solid texture, like an actual block of sky and cloud. If you "cut a sheet" of sky and display it as an image, you'd get ...
2
votes
1answer
1k views

Extracting perspective transformation from a 2D projection

I have a 2D projection of a flat, rectangular object in 3D space, like this one: I know all sorts of information about this shape—its opposite sides have the same length, the sides meet at right ...
0
votes
2answers
1k views

Any linear fractional transformation transforming the real axis to itself can be written in terms of reals?

I'm trying to teach myself complex analysis, and was reading about linear transformations. I would like to understand why any linear fractional transformation which transforms the real axis into ...
1
vote
2answers
116 views

Converting polynomials to depressed form

Given a polynomial of any degree $\sum_{i=0}^n a_ix^i$ can it be proven that the substitution $x=t-$${a_{n-1}}\over{na_n}$ will convert the equation to depressed form $b_nt^n$ + $\sum_{i=0}^{n-2} ...
0
votes
0answers
372 views

Joint distribution of transformed variables

I have a problem in deriving the transformed joint distribution for continuous random variables. The textbook says use jacobian which makes sense but I wanted to go from first principles like below... ...
0
votes
2answers
130 views

Transform/approximate this expression to avoid undefined value

I have an expression like this $$\sum_i^n\log\frac{x_i}{y_i}+\alpha\sum_i^nx_i\log\frac{x_i}{\beta}$$ A potential problem is that $x_i$ and $y_i$ may take value $0$ for certain $i$, hence making ...
2
votes
1answer
737 views

Isolate yaw-pitch-roll from rotation

I have a transformation that acts as such: $$RX=Y$$ Where $R_{3\times3}$ is a yaw-pitch-roll rotation matrix, and $X, Y$ are 3D vectors. Yaw ($\alpha$)-pitch ($\beta$)-roll ($\gamma$) rotations are ...
2
votes
2answers
253 views

Does this Laplace transform exist?

I had a final in differential equations with the first question being: "1. Does the Laplace transform of $\displaystyle \frac{1}{(1+t)}$ exist? Why or why not?" and number 2 was "2. If number one ...
2
votes
0answers
132 views

Hyperbolic Universal Covering Space

I have been working with Ricci flow in the euclidean and hyperbolic space but have been having considerable trouble determining how to generate a universal covering space for complex hyperbolic ...
0
votes
0answers
136 views

How do I transform the coefficients of a solved polynomial curve fit?

This all pertains to a piece of software I am writing but figured I'd get a better answer here than in Stackoverflow. I have no problem migrating the question if needed. Disclaimer: I am a software ...
2
votes
2answers
5k views

How to multiply vector 3 with 4by4 matrix, more precisely position * transformation matrix

All geometry in computer graphics are transformed by position * transform matrix; The issue is the fact that position is a vector with 3 components (x,y,z); And transform matrix is a 4 by 4 with one ...
0
votes
1answer
84 views

A few questions about linear transformations

$\phi \in \alpha(R^3,R^3)$ $B_c:\left(\begin{array}{rrr} 1&2&3 \\ 0&3&4 \\ -1&2&1 \end{array}\right) = [F]_C$ Determine the analytic form of the ...
1
vote
2answers
178 views

Modifying a discrete probability distribution according to set of weights

Given a discrete probability distribution (e.g., ${P_1=0.85,P_2=0.05,P_3=0.05,P_4=0.05}$), I would like to transform it according to some set of "weights" (say, ${w_1=2,w_2=0.5,w_3=1,w_4=0.5}$), which ...
1
vote
2answers
84 views

Transfer of random variables, uniqueness

If $X$ is a continuous random variable with known distribution, and $Y_1= f_1(X)$, $Y_2= f_2(X)$ where $f_1$ and $f_2$ are strictly increasing functions and distribution of $Y_1$ and $Y_2$ is the ...
4
votes
0answers
216 views

how do you map a sphere to a cube

I want to map a sphere to a cube in order to create a panoramic tour like the one given here But I don't know how can you obtain images like This image is one of the cube's faces. What I tried was ...
3
votes
1answer
98 views

random variable transformation

I'm having trouble with the following random variable transformation: $Y = X^2 + X$ I am looking for the pdf of Y. I tried the following method: $p_Y(y) = \int_{X} p_{Y|X=x}(y)\cdot p_{X}(x)dx$ and ...
2
votes
3answers
370 views

Permutation as Linear Transformation

Could you help me please to move forward with the problem. I'm trying to show that a function $\varphi_{\sigma }: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}$ $\varphi_{\sigma }(x_{1}, x_{2}, ... ...
1
vote
1answer
121 views

Finding the equation of plane that is transformed to a line

Suppose I have a transformation $T:\mathbb{R}^3\rightarrow \mathbb{R}^2$ and its matrix: $$T=\begin{bmatrix} 1 & -1 & 1\\ -1 & 0 & 1 \end{bmatrix}$$ I am told that there is a ...
3
votes
1answer
131 views

Elementary matrices

Is there a way to visualize the action of elementary matrices? (Or perhaps matrices in general). Perhaps someone could give an intuitive view of the effects of elementary row operations. Actually I ...
1
vote
0answers
76 views

Questions about interpolating translated points from a grid

I would like to do the following transformations on a very low resolution bitmap (64x64 pixels). I am doing this transformation on a computer images, but it has nothing to do with computers, you can ...
1
vote
1answer
47 views

Where have I gone wrong? — operators wavefunctions, etc

Aim: Show that $-{\hbar^2\over 2m} {d^2\over dx^2}\psi(x)-{\hbar^2\over m}\mathrm{sech}^2(x)\psi(x)=E\psi(x)$ is equivalent to $\hat{O}^\dagger\hat{O}\psi(x)=({2mE\over \hbar^2}+1)\psi(x)$ where ...
1
vote
2answers
265 views

Graphing Transformations. Why does the +2 in $f(x) = \sqrt{-x + 2}$ not work as expected when done out of order?

Graphing $f(x) = \sqrt{-x + 2}$ from the graph of $y=\sqrt{x}$. Correct Method First graph $f(x) = \sqrt{x}$. then $f(x) = \sqrt{x+2}$ (shift left 2) then $f(x) = \sqrt{-x+2}$ (Reflect over ...
1
vote
2answers
694 views

Decomposition of a unitary matrix via Householder matrices

If $U$ is unitary, how can I show that there exist $w_{1},w_{2},...,w_{k}\in \mathbb{C}^{n}$, $k\leq n$, and $\theta_{1},\theta_{2},...,\theta_{n}\in \mathbb{R}$ such that $U=U_{w_{1}}U_{w_{2}}\cdots ...