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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1answer
379 views

2D transformation

I have a math problem for some code I am writing. I don't have much experience with 2D transformations, but I am sure there must be a straight-froward formula for my problem. I have illustrated it ...
3
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2answers
6k views

How do I rotate a matrix transformation with a centered origin?

This is actually something I'm doing in Objective-C programming, but since it's very math-oriented I thought I'd post it here. I was reading up on linear transformations: ...
4
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2answers
2k views

Why composite transformations are multiplied to the right side?

I have seen that many composite transformations have the later transformation multiplied to the right side of the matrix. Say I have matrix an existing transformation matrix $\mathbf{M}$ and then ...
2
votes
1answer
375 views

Sum of projections

Let $E_1$ and $E_2$ be projections on $V$, a vector space over $F$. Why is if $\operatorname{char}F\neq2$ then $E_1+E_2$ is a projection iff $E_1E_2=E_2E_1=0$ ?
0
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1answer
100 views

2D transformation without rotation

Is there a name for 2D transformation with the least squares adjustment having the following parameters: shift_x, shift_y, scale. Transformation does not use any rotation... Thanks for your help.
0
votes
1answer
433 views

Decompose rigid motion affine transform into parts

I have an affine transform from $R^3$ to $R^3.$ It is described as Rotation about Z axis, rotation about X axis, a translation, rotation about Z axis, and lastly a scaling (same in all 3 dimensions). ...
5
votes
2answers
263 views

Transformations that leave a binomial distribution invariant

The binomial distribution is written as $$p(r|n,\theta )=\binom{n}{r}\theta ^r(1-\theta )^{n-r}$$ where $n$ is a positive integer, $0\leq\theta\leq1$, and $r$ is an integer taking values from $0$ to ...
3
votes
1answer
432 views

Invariants of a Reynolds stress tensor

I am dealing with a Reynolds stress tensor, which arises in Navier-Stokes equations and is symmetric. By using an Ultrasound based instrument, I can read the velocity components of the fluid along ...
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3answers
316 views

Get number of elements of a square matrix given a vector that has upper right elements of that matrix

Suppose I have some vectors: $[1,2,1]$ its length is $3$ wich represents a matrix like $\begin{pmatrix} 1 & 2\\ -1 & 1 \end{pmatrix}$ the complete matrix would have $4$ elements ...
2
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0answers
362 views

How to find the center of an (scaled) ellipse?

This question is an extension of How to find the center of an ellipse?. The solution there works well, but in Javascript the floating point calculations are not that accurate. The workaround is to ...
1
vote
2answers
290 views

Calculate nearest spherical harmonic for a 3d distribution over a grid?

I have a set of solutions to an equation, which are all very similar to spherical harmonics. The solutions are discretised on a regular 3d grid. I would like to label them with which spherical ...
2
votes
1answer
398 views

Translation of a mathematical statement formulated in words to one formulated in predicate logic

I want to express the fact that for all $x \in A$ that have the property that for all $y\in x$ $T(x,y)$ is true and there exists an $u \in B$ such that $P(y,u)$ is true AND for all $v\in C$, $Q(y,v)$ ...
5
votes
1answer
828 views

Using quaternions instead of 4x4 matrices for transformations

I'm interested in implementing a clean solution providing an alternative to 4x4 matrices for 3D transformation. Quaternions provide the equivalent of rotation, but no translation. Therefore, in ...
4
votes
5answers
481 views

Help a newbie understand Linear Algebraic terms

I am taking a class in Algebra but I am having a problem grasping exactly what it is I am being asked to do -- I think I am having a problem with the vocabulary being used. I have a couple of ...
0
votes
2answers
1k views

How to find the triangle matrix of a given matrix?

I read http://en.wikipedia.org/wiki/Triangular_matrix, and it says a matrix is triangularisable. But I did not find any where talking about how to do that. E.g. how can I transform this matrix into a ...
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2answers
3k views

Simple shape rotation

I feel like an idiot for asking, I got this question in a practice paper, it's the first question so it's easy. The question is "describe fully the single transformation that will map shape P onto ...
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4answers
1k views

How does multiplying by trigonometric functions in a matrix transform the matrix?

I found this comic: But I can't understand the humor because I can't understand how trig functions affect matrix multiplication. Can someone please explain?
3
votes
1answer
344 views

How can I calculate the transformation between two 3D triangles?

I am given the $3$-D coordinates of two triangles. For example: for $\triangle ABC$, the coordinates are: $A=(0, 0, 0)$, $B= (3.37576, 0, 0)$, $C=(5.14131, -2.47202, 0)$ and for $\triangle ...
0
votes
3answers
61 views

Average of several points after non-linear function

The application of this problem is in bioinformatics, but the problem itself is a general math one, I think. I have a function that converts a sequence score to a value in time units. This function ...
3
votes
2answers
277 views

Why can any affine transformaton be constructed from a sequence of rotations, translations, and scalings?

A book on CG says: ... we can construct any affine transformation from a sequence of rotations, translations, and scalings. But I don't know how to prove it. Even in a particular case, I found ...
1
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0answers
122 views

Efficient way to recompute weights when shifting range of Legendre polynomial bases

I am storing a 2D (Cartesian) density function as a 2D patch with known X/Y limits and a set of 11 coefficients of the third order 2D Legendre polynomial basis functions over that patch. This works ...
0
votes
1answer
88 views

Getting 5 or 7 and returning the opposite? [closed]

I get 5 or 7 and if i get 5 i need to return 7 if i get 7 i need to return 5. i need to do this in 1 mathematical formula. I have those: 12 - x 35 / x There ...
2
votes
2answers
455 views

Transformation and Matrices - Points and Vectors

Right question, I am stuck. We have been working on matrices and I think I understand them, however I have no idea how to apply these to this transformation question. Consider the points O = (0; 0; ...
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vote
1answer
620 views

How can I calculate the transformation of two 3D triangles?

Given two triangle I have the transformation (three rotation followed by three translation)of both the triangles. How can I calculate the transformation between two triangles? A numerical example will ...
1
vote
1answer
318 views

correct rotation and translation matrices

I wrote a C++ program that can calculate the magnetic field $\bar{B}$ generated by a circular coil that is placed in the origin, for a given point $\bar{P}$ in 3D ...
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1answer
426 views

Question about Rotational Transformation

My notes on Transformations has the following formula for rotating a point counter-clockwise about the origin: $\begin{align*}x^\prime&=x\cos\theta - y\sin\theta\\y^\prime&=x\sin\theta + ...
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vote
2answers
126 views

Arithmetic error when calculating inverse of the logistic?

I would like to rearrange the logistic function: $$y=\frac1{1+\exp(-a+bx)}$$ To calculate $x=f(y)$ So I did the following: $$\frac1{y}=1+\exp(-a+bx)$$ $$\ln\left(\frac1{y}-1\right)=-a+bx$$ ...
0
votes
1answer
521 views

how to perform a rotation around a point which itself is rotating?

I'm working on rotating human limbs in a 3d game. I use Linear Algebra matrix rotations and translations to achieve moving the human and limbs. I currently can rotate around a pivot point by first ...
4
votes
4answers
8k views

How do I convert the distance between two lat/long points into feet/meters?

I've been reading around the net and everything I find is really confusing. I just need a formula that will get me 95% there. I have a tool that outputs the distance between two lat/long points. ...
3
votes
2answers
1k views

Rigid Motions - The product of two rotations around different points is equal to a rotation around a third point or a translation

I'm having some difficulty wrapping my head around rigid motions in a plane. In particular, I'm trying to solve this following problem: In a Euclidean plane, show that the product of two rotations ...
7
votes
6answers
2k views

Find eigenvalues of a projection and explain what they mean

Suppose B represents the matrix of orthogonal (perpendicular) projection of $\mathbb{R}^{3}$ onto the plane $x_{2} = x_{1}$. Compute the eigenvalues and eigenvectors of B and explain their geometric ...
2
votes
2answers
587 views

If the image of a set is linearly independent, is the set linearly independent?

Suppose that $T: \mathbb{R}^m \to \mathbb{R}^n$ is a linear transformation and that $v_1, v_2, \ldots, v_p$ are vectors in $\mathbb{R}^m$. If $W = \{T(v_1), T(v_2), \ldots, T(v_p)\}$ is linearly ...
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votes
6answers
9k views

Finding a Rotation Transformation from two Coordinate Frames in 3-Space

The question I'm trying to figure out states that I have 3 points P1, P2 and P3 in space. In one frame (Frame A I called it) those points are: Pa1, Pa2 and Pa3, same story for Frame B (namely: Pb1, ...
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1answer
249 views

Rotation matrices for arbitrary dimensions

I initially asked this question here, and someone suggested this may be a better place to get an answer. I have a question about a rotation matrix, which can be represented in 2 dimensions as: ...
2
votes
2answers
650 views

Sketching vector diagram

I need to sketch a diagram which shows what happens when a 2x2 matrix is applied to a lattice. What would be the best software to perform such a thing?
2
votes
2answers
414 views

What are transformations in mathematics?

I'm learning about transformation in mathematics in general. There are many of them like for example Jacobian (which I'm trying to understand now). The "how ?" part is very easy. There are formulas ...
4
votes
2answers
799 views

Transformation T is… “onto”?

I thought you have to say a mapping is onto something... like, you don't say, "the book is on the top of"... Our book starts out by saying "a mapping is said to be onto R^m", but thereafter, it just ...
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vote
2answers
139 views

Can the inverse of this logit-like transformation be stated analytically?

For $\alpha \geq 0$ the transformation $x \mapsto \log(x) - \alpha \log(1-x)$ maps the unit interval to the real line (in fact for $\alpha = 0$ the transformation is not surjective). For $\alpha=1$ ...
3
votes
4answers
4k views

Show that the linear transformation T is invertible

(Application of the rank-nullity theorem) Suppose $S,T: V\to V$ are linear transformations of a finite dimensional vector space $V$, and that the composition $ST\colon V\to V$ is invertible. Show ...
2
votes
3answers
244 views

Applying a linear transformation to time sequences to separate interfering oscillations

This is an applied problem, which arises from the problem of reorienting of a sensor axes according to particle displacement directions: Consider a sensor which is located inside the solid substance. ...
0
votes
2answers
188 views

Writing an Integral in Different Form?

Is it possible to write $\int_{-\infty}^\infty e^{-iqu}\left( \frac{A}{\sqrt{1-iau}}+\frac{B}{\sqrt{1-ibu}}\right)^Ndu$ in this form $\int\frac{e^{-iu}}{(\sqrt{1-iau})^n(\sqrt{1-ibu})^m}du$
4
votes
4answers
266 views

Can anybody explain how these logarithms are transformed?

I'm learning for my algorithms exam and I can't derive two logarithm transformations: $ 3^{log_{4}(n)}=n^{log_{4}(3)} $ $ log_{3}(n)=log_{3}(e)*ln(n) $ I'm not very strong in logarithms, anybody ...
1
vote
2answers
110 views

Can any statement be made on the structure of a diagonal matrix after an unitary transformation?

Let $U$ be unitary and $D$ be diagonal. Can anything be stated about the structure of $$U^\dagger D U$$ then? Also, would this change for an infinite matrix, i.e. a discrete linear operator?
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vote
0answers
216 views

Fitting projective transformation

Given set of points in $3D$ ( $X = (x_1, x_2, x_3)$, $Y = (y_1, y_2, y_3)$ ), how can I fit transformation from $X$ to $Y$? As far as I know this is called projective transformation. Here is example ...
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vote
1answer
2k views

Determine scale factor of an object given its distance from a viewer/camera

I have a 3d object which in its simplest form consists of an origin in 3d space and a set of vertices that are all local to this origin. I then transform this 3d origin into 2d camera coordinates ...
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2answers
9k views

extracting rotation, scale values from 2d transformation matrix

How can I extract rotation and scale values from a 2D transformation matrix? ...
2
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2answers
409 views

Matrix transformation notation

I have a question about a transformation of a matrix. Lets say we have the following matrix $ M = \left[ {\begin{array}{cc} 4 & 3 \\ 4 & 3 \\ \end{array} } \right] $ Then I want ...
4
votes
0answers
175 views

What is known about the transformation of a power series in which $z^n$ is replaced with $z^{n^2}$?

Say we have the function $$G(z) = \sum_{n \geq 0} g_n z^n.$$ Is there a name for the transform T defined so that $$(T(G))(z) = \sum_{n \geq 0} g_n z^{n^2}?$$ Is there anything known about this ...
1
vote
1answer
131 views

How do I invert this transform?

Given a diffusion $dX_t = \mu(X_t)dt + \sigma(X_t)dW_t$, if one applies the transform $f(x) = \int_a^x \frac{1}{\sigma(u)}du$, one can use Ito's lemma to show that $df(X_t) = \left( ...
6
votes
1answer
506 views

A limit and a coordinate trigonometric transformation of the interior points of a square into the interior points of a triangle

The coordinate transformation (due to Beukers, Calabi and Kolk) $$x=\frac{\sin u}{\cos v}$$ $$y=\frac{\sin v}{\cos u}$$ transforms the square domain $0\lt x\lt 1$ and $0\lt y\lt 1$ into the ...