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
0answers
9 views

Is there a transformation which can make a matrix time-commutative?

Written out explicitly, the question I'm asking is: Given some square matrix $\mathbf{A}(t)$ , I'd like to find a transformation from $\mathbf{A}(t)$ to $\tilde{\mathbf{A}}(t)$, a square matrix of ...
0
votes
0answers
9 views

Transfer Function of non-linear systems

I am trying to find an approximate transfer function of the following system using either Laplace or Fourier transform methods $$\frac{dy(t)}{dt} = k_1\times q_0\times x(t)-k1\times x(t)\times ...
0
votes
1answer
26 views

Proving that a transformation of a function gives a positive result

If $x$ is real and: $$p = \frac{3(x^2+1)}{2x-1}$$ Prove that: $$ p^2-3(p+3)\geq 0$$ I think this has something to do with equating the discriminant to $0$, but I'm not entirely sure I'd really ...
1
vote
1answer
34 views

$X$ and $Y$ are ind. exponentially dist. ran. variables w/para. $\beta_1$ and $\beta_2$. Let $U=X+Y$, verify that $f_u(u)= \int_0^u f_{xy}(u-v,v)dv$.

I am a little lost with transformations with exponential distributions, any help would be much appreciated! The given hint is $0<x<infty$ and $x=u-v$
0
votes
1answer
12 views

Transformation matrix for a 3d->2d projection

We know $\mathbf{\hat{y}} = X\mathbf{w}$ and $A$ is the subspace in which $\mathbf{\hat{y}}$ lies (so the columns of the $X$ matrix define the subspace $A$). $\mathbf{\hat{y}}$ (2-dimensional vector) ...
-2
votes
0answers
32 views

Linear transformation in a basis [on hold]

Given: $ \varphi : \mathbb{R}^3 \rightarrow \mathbb{R}^2$ and $\varphi(x_1,x_2,x_3)=(x_1-x_2+4x_3,-3x_1+8x_3)$ Let $A=\{(3,4,1),(2,3,1),(5,1,1)\}$ and $B=\{(3,4,1),(2,3,1),(5,1,1)\}$.Find ...
0
votes
3answers
23 views

Linear transformation formula

How to find formula for linear transformation $\varphi : \mathbb{R}^2 \rightarrow \mathbb{R}^4$ when the following is given: $$\varphi ((5,1))=(2,5,1,1)$$ $$\varphi((1,0))=(3,4,2,2)$$ What is the ...
0
votes
1answer
26 views

How to apply coordinate transformations

Lets say I want to rotate a parabola by $\pi/4$ degrees counterclockwise. Wikipedia tells me a counterclockwise transformation would mean: $$ x'=x\cos t-y\sin t \\ y'=x\sin t+y\cos t $$ however ...
0
votes
0answers
16 views

Multiplication order for coordinate frame transformations

Suppose I have three coordinate frames: $A$, $B$ and $C$. If $T_{AB}$ is the transformation from $A$ to $B$, then which of the following is correct? $T_{AC} = T_{AB} \cdot T_{BC}$ $T_{AC} = T_{BC} ...
1
vote
1answer
21 views

Minimum amount of points required to find a transformation matrix

Given a set of point $P$ in $\mathbb R^n$ and the same set of points $P'$ which have been transformed by a transformation matrix: $$L: \mathbb R^n\mapsto \mathbb R^n$$ $$L(p_1) = p_1',\;\; p_1\in ...
0
votes
0answers
8 views

Non-linear transformation of symmetric distribution to get non-negative skewness

Say you have a variable $x \sim D(\mu,\sigma^2) $, where $D$ is a symmetric known distribution. I'm looking for two linear or non-linear transformations of $x$ that give one negative and one positive ...
0
votes
0answers
10 views

It's nonsingular [closed]

Is it possible to prove that if a certain partial differential equation is elliptic or hyperbolic I can find the canonical transformation to be nonsingular? Namely, I need to show that the Jacobian J ...
0
votes
0answers
15 views

what are the applications of linear transformations in civil engineering [closed]

i wanted to know the applications of linear transformations, Eigen value problems and singular value decomposition in civil engineering
0
votes
1answer
24 views

Show that $F$ is not a one-to-one transformation

Given $$F(x,y)=(x-y,y^2-x-2)=(u,v),$$ how to show that this transformation is not one-to-one? And at which points $F$ is locally one to one? While I was drawing this transformation I found that ...
0
votes
0answers
14 views

When creating conformal images, how do you change the basis of the input lattice such that spirals result in the transformed image?

I am trying to emulate the results shown in the Wikipedia page on Conformal Images in an attempt to better visualize complex functions (and stare at some trippy images, man). The script I wrote ...
1
vote
1answer
24 views

Apply Cayley transformation on vector x

If I have $Q = (I + S)(I - S)^{-1}$ ($Q$ is the Cayley transformation of skew-symmetric matrix $S$) then how do I construct a rank-2 $S$ such that $Qx$ has all zeros except the first component?
1
vote
1answer
26 views

Cayley transformation of a skew-symmetric matrix is orthogonal?

If $S$ is skew-symmetric ($S^{T} = -S$), how do I show that $Q$ is orthogonal where $$Q = (I + S)(I - S)^{-1}$$ which is the Cayley transformation of $S$.
-1
votes
3answers
38 views

Need help with linear transformations (with projection and reflection)?

Let $L$ be the line given by the equation $4x − 3y = 0$. Let $S : \mathbb{R}^2 \rightarrow \mathbb{R}^2$ be reflection through that line, and let $P : \mathbb{R}^2 \rightarrow \mathbb{R}^2$ be ...
0
votes
1answer
25 views

Solving a transformation equation involving vectors and quaternions

I'd like to solve the following equation for $c$, where $a$, $c$, and $d$ are position vectors represented by quaternions with $w$ (the real component) set to $0$ and $b$ is a unit quaternion: ...
0
votes
0answers
15 views

Finding the Transformation given the domain and the codomain in $\Bbb R^3$

So I am given the domain and the codomain of three matrices such that the $F: \Bbb R^3 \to \Bbb R^3$, $T(1,0,-1) = (2,2,1)$ and $T(1,1,0) = (1,1,0)$, the point here and the question rather is not to ...
0
votes
0answers
35 views

How does one find the cdf of this transformation? [closed]

$ \text{ Let X be some r.v. with Support } (0,\infty), \text{ and let } v \in (0,1), \quad n,m \in \mathcal{Z} $ Then we define, $ Z = \begin{cases} 0, & \text{if X<m} \\ v^X, & ...
0
votes
0answers
13 views

How do I compute uncertainties in the positions transformed using Helmert transformation?

I am familiar with Python, MATLAB and Mathematica. My data is given by Cartesian coordinates (positions in X,Y,Z (meters), standard deviations XX, YY, ZZ (meters) and a correlation matrix (XY, YZ, ...
1
vote
1answer
80 views

Difference between transform and transformation.

I was told that there is a difference between a transform and a transformation. Can anyone point out clearly. For example : Is Laplace Transform not a transformation ?
0
votes
0answers
15 views

How to formulate a coordinate transformation

Thank you in advance for taking the time to consider this. I'm trying to figure out how to formulate a coordinate transformation problem (at least that is what I think it is). Background: I have an ...
1
vote
1answer
17 views

Perspective transformation matrix application

I need to transform an angled photographed pice of paper to a "flat" image. I found this question & solution here on Mathematics and tried it out for the image given in the solution: The values ...
0
votes
0answers
16 views

Syncronize positions of 2 rectangles with different origin point while rotation

Suppose we have 2 rectangles in Cartesian coordinate system with (0,0) at the top left corner of the screen. Both of rectangles (a and ...
0
votes
1answer
12 views

Equations transformations with roots

How does the following transformation works (do not write that it is easy i want the answer): $$\ln \sqrt[n]{\frac{n!}{n^n}}=\frac{\ln \frac{n!}{n^n}}{n}$$
0
votes
0answers
11 views

Finding the relative pose of a robot gripper

I have a robot arm with a gripper. I know the gripper pose (relative to the robot base coordinate system) at any moment. At startup, I record the pose of the gripper and set this as the original pose ...
1
vote
2answers
35 views

Formula for the sum of fractions [duplicate]

How to find the formula for the sum of fractions like this? $$\frac{1}{1\times 2}+\frac{1}{2\times 3}+\ldots+\frac{1}{n\times (n+1)}=$$
1
vote
2answers
26 views

Transformations of inequalities [closed]

How from $$\frac{x^{n+1}+y^{n+1}}{2} \ge \frac{x^n+y^n}{2} \times \frac{x+y}{2}$$ this inequality we can obtain this $$x^{n+1}+y^{n+1} \ge yx^n+xy^n$$
0
votes
1answer
32 views

Making sense of polar coordinates transformation on the derivatives

I would like to make sense of the transformation of the differentials in polar coordinates (to fix the ideas). To be more precise, the "right" way to find the transform for the differential and the ...
1
vote
2answers
35 views

Cayley Transform and Eigenvalues

I have a particular operator, namely $A=-i\frac{d}{dx}$ that I would like to Cayley transform. $A$ is defined on the Hilbert space $L^{2}[0,1]$ and has domain $\mathcal{D}_{\alpha}=\{g:g \in ...
2
votes
1answer
24 views

Rotate a vector about a given axis by the use of a quaternion

I encountered a problem in programming where I need to rotate a given vector about a given angle. To be precise, I need to change it to a quaternion so that I can later change it to a 4x4 matrix to ...
0
votes
0answers
29 views

Rotational matrix problem?

In the problem yo-yo is made of two identical cylinders of radius $R$, thickness $h$ and mass $M$, and the yo-yo is let go. In order to define the position of the yo-yo, I need as position vector and ...
0
votes
1answer
21 views

Normal distribution

X follows a regular normal distribution on V with center $\xi$ and inner product $<\cdot,\cdot>$, and let $\eta \neq 0$ be a vector in V. Show that the reel stochastic variable ...
0
votes
1answer
31 views

Changing $[0,2\pi)$ with $S^1$ such that a map defined on $[0,2\pi)$ stays unchanged

* Consider the following procedure of changing the domain of a map, but the map remaining essentially the same - illustrated, for concreteness, in case of the polar-coordinates map.* Let ...
0
votes
1answer
22 views

Fourier Transform - Laplace Transform - Which variable transform?

I need to know when do I have to transform $x$ and when $y$ in a PDE in Fourier Transform and Laplace Transform. In an exercise of Fourier Transform, I have to solve a Laplace Equation, where ...
2
votes
0answers
25 views

Laplace Transforms [closed]

All I'm asking for a link on this (if, any) to which I could be directed to solve some hard questions on Laplace transforms. (with some other advanced material regarding the same)
0
votes
1answer
22 views

Lotka-Volterra coordinates transformation

I would like to ask the following: Given a Lotka-Volterra predator-prey system, \begin{align} & \frac{dx}{dt}={\alpha}x-{\beta}xy \\ & \frac{dy}{dt}=-{\gamma}y+{\delta}xy \end{align} , with ...
0
votes
3answers
67 views

Dimension of Hom(U,V)

I know this has been asked before - I am really struggling to understand what people have said though, so I want to ask for myself. If U,V are vector spaces over field K, with dimensions n,m ...
0
votes
0answers
27 views

Transfer function: steady-state solution of equation

Place the transfer function in the form $$H(i\omega) = \frac {1}{R}e^{-i\phi}$$ and use this result to find the steady-state solution of the equation$$x'' + x'+4x = 3*cos(2t)$$ I don't really ...
2
votes
1answer
45 views

Fourier COSINE Transform (solving PDE - Laplace Equation)

I'm trying to solve Laplace equation using Fourier Cosine Transform (I have to use that), but I don't know if I'm doing everything OK (if I'm doing everything OK, the exercise is wrong and I don't ...
-1
votes
0answers
29 views

How can I show that the AR process is nonstationay if x(n) has nonzero mean?

This is a first-order-real-valued autoregressive (AR) process $y(n)$ that satisfies the real-valued difference equation $y(n)+a_1y(n-1)=x(n)$ where $a_1$ is a constant and x(n) is a white noise ...
1
vote
0answers
22 views

How to apply the chain rule for partial derivatives to transformations?

I'm currently working to solve the Black-Scholes model partial differential equation (it's a model for a.o. stock option prices). The Black-Scholes equation for a calloption C(S,t) is given by $ ...
0
votes
0answers
12 views

How to understand all types of transforms as linear operators on function spaces?

I would really appreciate if someone can point to a simple general framework that can help me to understand integral transform from a generalized point of view so that there is no longer a fourier ...
0
votes
0answers
27 views

Prove a formula after change of variable?

If I have a change of variable $(x,u)\to (X,U)$ given by $$X=x+\epsilon u,U=u-\epsilon u.$$ How to prove the formula $$\frac{\partial U(X,0)}{\partial \epsilon}=\phi(X,u(X))-u'(X)\xi(X,u(X)),$$ where ...
0
votes
1answer
19 views

Cross-sectional function for a surface of revolution

If I take a one-to-one function $f(x)$ and rotate it about the x-axis, how can I describe a function resulting from a cross-section of the solid of revolution? I'm not talking about the circular ...
0
votes
0answers
10 views

Shear matrix simple explanation

I can understand translation, dilation and rotation matrices, but the shear one is still obscure to me (despite understanding what shearing means graphically). This is the matrix: ...
2
votes
3answers
36 views

How does $(x+3)^2 - 2^2$ become $(x+1)(x+5)$?

I don't understand how $(x+3)^2 - 2^2$ can be transformed to equal $(x+1)(x+5)$. A short demonstration and/or reference to math rules would be very kind. Thanks.
1
vote
1answer
32 views

Transformation Matrix for cube in 2D

My task is to transform the cube from the left corner to the big cube in the middle: What I did was: First i scale the cube: $$ \begin{pmatrix} 4 & 0 & 0 \\ 0 & ...