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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Real linear tranformation

When do we say that a transformation $T$ which takes the complex number field onto itself is real-linear? I need to know it for my homework but I can't seem to find the definition anywhere.
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Question on linear algebra mappings

If $T:R^m\to R^n$ is a linear transformation, show that there is a number $M$ such that $|T(h)|\leq M|h|$ for $h\in R^m$.
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Equality of two Determinants (transformation)

$det\begin{pmatrix} -\lambda & 1 & 1 & 1\\1 & -\lambda & 1 & 1\\1 & 1 & -\lambda & 1\\1 & 1 & 1 & -\lambda\\\end{pmatrix} = ...
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75 views

Equation for a sphere after a projective transformation?

I was wondering if there is a general equation for a sphere that has undergone a projective transformation (i.e, the sphere has been multiplied by a 4x4 homography matrix)? I attempted to multiple ...
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1answer
38 views

What is the difference between the terms transformation and map?

Recently I noticed the usage of map in my topology book, and got confused because I already saw the term transformation somewhere. Both have the form $T:a\to b$, so what is the difference? Are they ...
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50 views

$T: \mathbb R^n \to \mathbb R^n$, $\langle Tu,v\rangle=\langle u,T^*v\rangle$, is $T^*=T^t$ regardless of inner product?

Basic question in linear algebra here. $T$ is a linear transform from $\mathbb R^n$ to $\mathbb R^n$ defined by $T(v)=Av$, $A\in \mathrm{Mat}_n(\mathbb R)$. We are given some inner product $\langle ...
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2answers
171 views

Coordinates rotation by $120$ degree

If I have a point on a standard grid with coordinates say: $A_1=(1000,0)$ $A_2=(707,707)$ Is there a easy way to transfer this points to $\pm 120$ degrees from the origin $(0,0)$, and ...
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1answer
123 views

Inverse Function + Reflection In Y-Axis

Not getting any of the answers in MC. Is the answer wrong, or have I done something wrong?
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18 views

continuing and injective transformation

Does exist continuing and injective transformation B->A ? Are they homeomorphic?
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654 views

Finding equation of the image under a linear transformation

The equation of C is $x^2 + y^2 =1 $ How do I find the equation of the curve $C'=f(C)$ This is the image of $C$ under the linear transformation $f$ represented by the matrix $A=\begin{bmatrix}2 & ...
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116 views

$3$D transformation matrix to $2$D matrix

I have a $3$D affine transformation $4\times 4$ matrix. I need to convert it (project) to a $2$D affine transformation $3\times 3$ matrix, which looks like this: $3$D rotations are irrelevant and ...
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110 views

Why a 2D Affine Transformation matrix is 3 by 3

The matrix which I get for Scaling , Shearing and Rotation are follows: Scale: Shear Rotation Why do we need Homogenous Co-ordinate to get the transformation matrix as listed below? (need a ...
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118 views

Get 2D coordinate transformation matrix based on points in a system and their angles in the other?

I'd like to get the parameters (rotation angle,$\Theta$, and translation coefficients, $x_0$ and $y_0$)) of a transformation for translating and rotating points in a coordinate system to another. As ...
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368 views

Jacobian of Fourier Transformation

I am trying to calculate the Jacobian determinate of the Fourier transform which I stumbled upon when studying the Path Integral in Quantum Field Theory. I know the answer should be $1$ but I don't ...
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1answer
14 views

when linear mapping keeps monotonicity of $L_2$ norm

Consider an arbitrary vector $\alpha$ from vector space $R^p$, a linear mapping $A: \alpha\rightarrow A\alpha$ transforms $\alpha$ to $A\alpha$ in space $R^q$. What condition should $A$ satisfy so ...
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1answer
22 views

Linear Transformation Problem Given 3 transformations

can anyone help me get started with this question. Right now I am guessing and checking which is not efficient. I figured out out that the transformation is (?,?,x-y-z) so far Let $T:\Bbb R^3\to ...
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1answer
34 views

Birational Transformations question

so I'm wondering, is there a birational transformation one can make to the equation $Y^2 = X^m + f_{m-1}X^{m-1} + ... + f_0$, where all $f_i \in \mathbb{Q}$ so it is of the form $Y^2 = X^m + ...
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25 views

Transform pdf in higher dimensions?

Seem to remember the following equation held: $f(u) = {dx\over du} f(x)$ if one is give the probability distribution of x and a relationship between x and u the pdf of u can be derived. Sorry can't ...
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38 views

What formula would you use to cast an average of several numbers into a smaller range?

Say I have four numbers ranging in value from 15-95. If I want to, for a simple example, say that if the average of the four numbers is 15 (lowest possible value), that would relate to 2 on a scale of ...
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1answer
112 views

Univariate and Matrix Representation of Affine Transformation

Let $\mathbb{F}$ be a finite field with $q$ elements and $\mathbb{E}$ an extension field of degree $n$ of $\mathbb{F}$. Let $S:\mathbb{F}^n\rightarrow \mathbb{F}^n$ be a affine transformation and ...
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82 views

For general non-symmetric square matrices is there a matrix norm that is invariant under similarity transformations?

I think that there is no similarity-invariant matrix norm for general matrices. But are there similarity invariant norms for special types of matrices (e.g. for matrices whose eigevalues are different ...
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How to find the values of transformstion and its center/axis? [duplicate]

I have system of two planes. Each plane is defined by three points, so I have their equations. One of these plane is stable, I can't perform any transformation. The second one is modifiable - rotation ...
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1answer
27 views

Linear Algebra Linear transformation Help

If $T:\mathbb{R}^n \rightarrow \mathbb{R}^n$ is a linear transformation, then there exists a basis for $\mathbb{R}^n$ in which $T$ is diagonal. Is this true or false
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Calculating with transformation matrix

Given is the transformation of coordinates $ T_{AB} = \begin{pmatrix} 1 & 1 \\ -1 & 1 \end{pmatrix} $. 1.) What are the new coordinates for the vectors (1,0) and (0,1)? It should be: $ ...
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Help Deriving the Canonical Form of this Elliptic PDE

So I'm given the following PDE, for which I'm to derive the canonical form: $$u_{xx} + u_{xy} + u_{yy} = 0.$$ Clearly $A=1, B=1/2$ and $C=1$. Hence we have $\xi_x/\xi_y = -1/2 ...
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finding this linear transformation

i am following this guide: http://www.calpoly.edu/~brichert/teaching/oldclass/f2002217/handouts/goof.pdf my question is to find the linaer transformation that adheres to $T(1,1,1) = (1,1,1)$ ...
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Plane transformations

I need help in understanding how plane transformations work: for example, let $$A = \{(x,y) \in \mathbb{R}^2: x^2 + y^2 < 1\}$$ Now let's change coordinates like this: $$x = u^2 - v^2$$ $$y = ...
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296 views

Givens rotation of the following vector of 3 elements.

I have to find the givens rotation matrix that will transform the following vector $[1, 1, -1]^T$ to $[y, 1, 0]^T$ (basically to insert a $0$ on the third position without altering the second one). I ...
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1answer
69 views

Find rotation angle of given image

At first: our aim is to find the total transformation of left house to the right house. What I did it first is translating the house with the center to the origin. I already found out that the ...
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2answers
334 views

Books on geometric transformations and/or analytic geometry?

I've been looking to expand my knowledge in geometry as it's not covered in my undergraduate curriculum. For some reason I'm repelled by the classical approach (hopefully it will pass) as I feel it's ...
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4answers
106 views

Quadratics, transformations, and formulas

Two-part question. Feel free to answer just one part, or both (write which letter part you are answering) a) If the quadratic function $g(x)=a(x-h)^2+ k$ does not touch the $x$-axis, what can be ...
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Find the transformation.

I have to define (find?) the linear transformation $ f:\mathbb{R}^{3}\rightarrow \mathbb{R}^{2} \ \ \ where:$ $f(1,1,0)=(1,1)$ $f(0,2,-1)=(-1,0)$ $f(1,2,-1)=(0,2)$ How to achieve this? It is hard ...
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1answer
853 views

Find kernel and image of linear transformation.

I am given transformation : $f:R^3 \rightarrow R^2$ $ f(x,y,z)=(-x+y+z,x-y+z)$ I am requested to find kernel and image of this transformation. I am finding kernel: $ (-x+y+z,x-y+z)=(0,0 )$ ...
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Transforming partial differential equations

$13.$ Consider the change of variables $$x = e^{−s} \sin t,\space y = e^{−s} \cos t, \space \text{such that} \space u(x,y) = v(s,t)$$ (i) Use the chain rule to express $∂v/∂s$ and $∂v/∂t$ in terms ...
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How to compute (and check) this transform matrix?

Background: This is a homework exercise which asks to compute a transform matrix. The answer has been published by our teacher. However, my approach goes a different way and gets a different solution. ...
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How to Evaluate $\int^\infty_0\int^\infty_0e^{-(x+y)^2} dx\ dy$

How do you get from$$\int^\infty_0\int^\infty_0e^{-(x+y)^2} dx\ dy$$to $$\frac{1}{2}\int^\infty_0\int^u_{-u}e^{-u^2} dv\ du?$$ I have tried using a change of variables formula but to no avail. Edit: ...
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Is it true that every orthogonal transformation , even over $\mathbb R$, is diagonalizable?

Is it true that every orthogonal transformation , even over $\mathbb R$, is diagonalizable? I didn't succeed to get any information about it. Could anyone explain please?
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How to use polynomial or conformal transformation

In my research, I came to a transformation problem. The simple version is an initial circle (or sphere) region is advected by some deformational flow. After some time the circle will be deformed into ...
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75 views

Jacobian of an inverse

Suppose that we have an invertible map $T(u,v)=(x,y)$. The Jacobian of $T$ is given by $ \text{Jac}(T)= \left| {\begin{array}{cc} x_u & x_v \\ y_u & y_v \\ \end{array} } ...
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Find conjugate transpose (adjoint) of linear transform

A difficult question I've been trying to tackle but I seem to hit a dead end. Let $V$ be an inner product space over $\mathbb R$. We are required to find $T^{*}$ such that $$\left<T(u),v\right> ...
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1answer
51 views

I need hints on showing a matrix with certain properties defines a special transformation

Given the matrix $$A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$$ with integer coefficients, rational eigenvalue, and determinant $1$, show $A$ acts as a shearing along its eigenvector. Here is ...
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1answer
26 views

Obtain hamiltonian from a lagrange functional.

Assume that we have a Lagrange functional $L = L(\psi, \partial_t\psi,\partial_x\psi)$ with $\psi:(x,t) \rightarrow \psi(x,t)$. From the this I want to calculate the Hamiltonian. I was wondering how ...
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3k views

How do I find transformation matrix with respect to standard basis?

I know that in order to find transformation matrix with respect to a basis, I need to apply the transformation to said basis and the result is the column of the transformation matrix. But what ...
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Show that T is a linear transformation and find a, b, c

I'm having trouble understanding this question and the proper way to solve it. I don't understand the solution given and why this was the right way to answer it. Problem: For the vector space ...
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1answer
73 views

Z-transform a transfer function

Could someone help me invers Z-transform of this transfer function. $H_k(z) = \frac{Y_k(z)}{X(z)} = \frac{1}{1-cos(\frac{2·\pi ·k}{N})·z^{-1}+z{^-2}}$
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If two sides of a triangle are equal, and the angle between them is $60^\circ$, prove the third side is equal to the first two sides.

In other words, given points $A$ and $X$. Rotate $X$ $\,-60^\circ$ around $A$ to get point $X'$. How would you prove $XX' = AX = AX'$? I know this is true.
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Small Lorentz Transformation

This is very simple and I can 50% understand it but would like to properly understand why it is. If we have an infinitesimal Lorentz transformation $\Lambda^\mu _\nu = \delta^\mu _\nu + \omega^\mu ...
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Calculating convolutions of probability density functions

I have a PDE: $$\frac{\partial N (x,u)}{\partial x}=\int _0^uN(x,u)f(u-u')du'$$ $$N(0,u) = \delta (u)$$ Here $f(u)$ is a probability density function for $0 \le u \le u_{max}$, $\int _0 ^ {u_{max}} ...
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Proving Kummer's Transformation

I'm working with a Kummer equation of the form: $z\frac{\partial^2 w}{\partial z^2}+(b-z)\frac{\partial w}{\partial z} -aw=0,$ which is solved by Kummer's Confluent Hypergeometric function: ...
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The image under mapping $w=(z+i)/(z-i)$, of the third quadrant?

The title says it all. I am not sure how to approach this problem. The only related problems i have done is mapping a (unbounded)line /circle to a line/circle. Regards Exatic