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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102 views

Transfer Transformation from Physics to Vector Graphic

Upfront, I am not a professional in Maths and hope that the formulation of my question describes the problem well enough. I am creating a jump'n'run game, which uses a physics engine (Box2D) and SVG ...
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3answers
41 views

$T:V \rightarrow V$ And $U \cap Ker(T)={0}$ prove that if$ (u_1,..u_n)$ linear Independent so does $T(u_1)…T(u_n)$

There will be $T:V \rightarrow V $ Linear Transformation U is sub-space of V so that $U \cap Ker(T)={0}$ Prove that if $(u_1,u_2,...,u_n)$ are linear independent so does $T(u_1),T(u_2),...,T(u_n)$. ...
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2answers
49 views

upper bound for equation

Let $0 < p < 1$ be some constant. I am looking for an $M$ such that $$f(n) = \left(1-p^{\log{n}}\right)^{n} < M(n)$$ I am looking for a tight bound, something of the form: $2^{-n/\log{ ...
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2answers
75 views

Existence of a linear transformation in an infinite dimension vector space.

If $V$ and $W$ are vector spaces, $\beta=\{v_1, \ldots , v_n\}$ is a finite a basis for $V$ and $\{w_1, \ldots , w_n\}\subset W$, we know there is an unique linear transformation $T:V\rightarrow W$ ...
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1answer
152 views

Expectation of (1/x)-1 possible transformation involved??

I'm a bit confused with the first steps in this problem: $F(x)=x^4$ for $0<x<1$ a) Find $E[(1/X)-1]$ b) Let $Y=(1/X)-1$. Find the support of $Y$, its pdf and CDF. Name its ...
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0answers
56 views

Transform recurrence relation

Is it possible to transform following recurrence relation $a_n=4a_{n-2}-a_{n-4}$, $a_0=1$, $a_1=0$, $a_2=3$, $a_3=0$ so that it will have nonnegative coefficients? Number of terms, of course, can be ...
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1answer
24 views

general rotations

Let $R$ be the rotation about the point $(1,0)$ by an angle of $45$ degrees. By using matrix methods: Find the image of the line $2x-3y+1=0$ under $R$ I would really appreciate it if someone ...
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1answer
636 views

How can I combine affine transformations into one matrix?

So from what I understand from this picture, the box is stretched to twice its width. And it is then flipped from the x-axis. And then it is rotated 30 degrees anticlockwise. So these three ...
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1answer
381 views

Find 2D affine transform matrix given a pair of points

I have the coordinates of two points in an initial 2d coordinate system and the corresponding coordinates in a target system. Is is possible to determine the affine transform matrix from these values? ...
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1answer
20 views

Function that transforms a Matrix to different dimensions

What is the name of a function that transforms a matrix into different dimensions? Say I have a matrix M of dimensions $(x,y)$ and I want to transform it to dimensions $(w,v)$. I can accomplish this ...
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1answer
59 views

Constructing a similarity matrix between points

I have two images with two sets of corresponding points. In order to align the images I'm trying to compute the similarity matrix that describes the relationship between the corresponding points. I ...
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78 views

Invariant functions under integral transforms

We all know Fourier transform has invariants such as $e^{-x^2}$, and another MSE post has shown the non-existence of invariant function under Hilbert transform using Fourier transform. I am wondering ...
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1answer
38 views

Show that $T$ is a linear transformation given Orthonormal basis

Suppose that $T:\mathbb{R}^n\rightarrow \mathbb{R}^n$ and suppose that $\{v_1,v_2,\cdots,v_n\}$ and $\{Tv_1,Tv_2,\cdots,Tv_n\}$ are orthonormal basis of $\mathbb{R}^n$. Prove that $T$ is a linear ...
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2answers
37 views

Diagonalization of a strange transformation

Let be $V$ a vector space on $\mathbb C$ and $\dim V=4$ and let be $f \in \operatorname{End}(V)$ such that $\operatorname{Im}(f^2+a \cdot \operatorname{id}) \subset \ker(f+id)$ where $a=\det f$, ...
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1answer
117 views

Linear Programming Transformations

What is the process of performing a transformation from a given problem to another linear programming problem such that the transformed problem has an optimal solution iff the initial problem has a ...
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2answers
69 views

Does congruence guarantee length conversion?

Suppose that a linear transformation $M:R^2 \rightarrow R^2$ maps a triangle $ABC$ to a congruent triangle $A'B'C'$ ($\{A, B, O\}, \{B, C, O\},\{C, A, O\}$ are not colinear, and $A,B,C\neq O$) Is it ...
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42 views

Determinant of a transformation matrix

I have been reading about determinants and transformation matrices. After that I was reviewing some exercises on a book I got. In one exercise I'm asked to find the transformation matrix and the ...
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1answer
25 views

About the matrix of two linear transformations

I have an exercise to answer, and I don't know if I've done it the right way. This is only a little part of the exercise, but I have to know if what I've done so far is correct. Here we go: Let $V$ ...
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3answers
61 views

Linear Algebra Vector Space matrix help

Let $M_{2\times2}$ be a vector space of all $2\times2$ matrices. If the transformation from $M_{2\times2}$ to $M_{2\times2}$ is $t(A)=A+A^T$ and $A$ is a $2\times2$ matrix with the top row $a,b$ and ...
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1answer
27 views

Increasing length of closed spline (scaling)

I have a 2D closed spline and I need to increase its total length by a factor k, without changing its curvature, basically scaling. If this spline was a circle, I ...
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1answer
40 views

Is it possible to prove a non linear transformation to linear transformation?

Is it possible to prove a non linear transformation to linear transformation.For example,F(x,y)=(3x,2xy).F(0,0) results linear transformation,but F(2,2) gives non linear transformation.Which result I ...
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0answers
59 views

Diagonalization of a linear transformation in the polynomial vector space

Let $V = R_3[X]$ be the vector space of polynomials with real coefficients of degree at most 3 and consider the linear transformation $V \rightarrow V$ defined by $f_a(p(x))=p(1-ax)$ for each $p(x) ...
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1answer
27 views

If $T,S \in L(V)$ are positive operators, how can I show that $TS$ is self-adjoint?

If we let $V$ be a finite dim. real/ complex inner product space, and $T \in L(V)$ and $S \in L(V)$ we let be positive operators, how can I prove that $TS$ is self-adjoint? I tried to decompose $TS ...
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1answer
99 views

Describing Cartesian transformations in Cylindrical Polar Coordinates

I have a question about converting functions defined in Cartesian coordinates to a cylindrical polar system. The particular coordinate transformation that I'm reading about is: \begin{equation} ...
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1answer
68 views

Linear Algebra - Understanding how to determine if a transformation is linear

I'm new to linear transformations in linear algebra and I can't quit understand how to find out if a transformation is linear. Any help would be much appreciated! a) $T:\mathbb R^3 \to\mathbb R^2$ ...
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1answer
16 views

How to name this transformation?

Let the transformation be $T:\mathbf s\to \mathbf s'$, where both $\mathbf s$ and $\mathbf s'$ are of the form $(s_0, s_1, s_2, ..., s_n)$, and $s_i'=a_is_i$ for each $s_i$ in $\mathbf s$ and its ...
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1answer
100 views

Big axis of an ellipse

I drew a circle in this square and I transformed them (view in 3d). How to find the angle between the big axis and $y$ or $x$ axis? Blue plane rotated by 36° around $y$ axis; azimut is 30° and ...
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1answer
47 views

$T$, $S$ are lineary dependent $\Leftrightarrow$ $[T]_B$, $[S]_B$ are lineary dependent.

EDIT: I see in the comments that my question is not clear enough so I will explain: if I want to check whether $T$, $S$ are linearly independent or not, I will just pick an easy to work with, basis ...
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1answer
31 views

Book recommendation for transformations.

Can I please get recommendations for books/notes on transformations? The topics covered should be Affine transformations Projective transformations Transformations in Euclidean space etc A ...
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60 views

Re-arrange expression to transformation form

$$\frac{6x-5}{3x+1}$$ How do you write this in the form $$\frac{b}{x+c} + a$$ I know how to find a (2) by asymptote theory, but I don't know how to re-arrange to find B.
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0answers
59 views

Linear Algebra Matrix Transformation Question

Can someone please help me out with this question. If a nonzero matrix $A$ is transformed from $\mathbb{R}^3$ to $\mathbb{R}^2$, then the null space of $A$ must be a one dimensional (sub)space of ...
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1answer
57 views

Rectangular transformation into Polar coordinates

I was working with a simple transformation of rectangular coordinates - symmetry around the y-axis, i.e. $$f(x,y) = (x, -y)$$ I wanted to express the identical concept in polar coordinates. After ...
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85 views

Algorithm to determine matrix equivalence

I'm a physicist who's not particularly good at linear algebra so please accept my apologies if this is standard textbook stuff that I'm just unaware of. I have two real rectangular matrices $A_{mxn} ...
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2answers
603 views

Approximate a polynomial function using a sum of sine waves

I have a polynomial function which I need to approximate by a sum of sine waves with constant amplitude along a given domain. From what I hear, this might be a good time to make use of Fourier ...
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1answer
23 views

Generate function from discrete data (time-series)

How to transform discrete data into continous function ? I am working extensively with time series data and I would like to reduce amount of data in our frontend application. It would be cool to ...
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1answer
129 views

Transforming a circle to get a parabola

On http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/geometry/geo-tran.html I am unable to understand the following point Obviously, this transformation sends (x,y,w)=(1,0,1) to (x',y',w') = ...
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1answer
119 views

Rotation formalisms in three dimensions

I'm little bit confused. The Rotations are described by various means Direction Cosines Matrix (DCM); Euler Angles; Euler Axis/Angle; Quaternion. What is the difference between them. How I can ...
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0answers
250 views

Describing transformations using base vectors

So I just learned that we can describe vector transformations of shapes using base vectors, where the base vector I = $$ \begin{pmatrix} 1 \\ 0 \\ \end{pmatrix} $$ and J=$$ ...
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2answers
177 views

Prove that the following matrices cannot represent the linear transformation $T$ in ANY basis

$T: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ defined as $T(x,y,z) = (2x,z,y)$ is a linear transformation. I need to prove that the following matrices cannot represent $T$ in ANY basis: ...
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1answer
55 views

What is/are the algebraic equation(s) for transforming a unit square into a specific parallelogram?

Goal: To transform a unit square into a parallelogram in which (a) the diagonals are parallel to the unit square's diagonals, (b) the longest diagonal is equal in length to either of the unit square's ...
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2answers
179 views

Linear Algebra One to one and onto function

I was just wondering how I can tell if a function is onto. $\mathbf{R}^3\to\mathbf{R}^1$ Lets say the standard transformation matrix has vectors $\{1,0,0\}$, $\{0,1,0\}$, $\{0,0,0\}$. I know that this ...
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1answer
40 views

Linear transformation and linear subspaces

Let $T:V\rightarrow V$ bwe a linear transformation. Let $L \subset V$ be a linear subspace such that $L \cap \text{Ker}\,(T)=\{0 \}$. Prove that the image given by T of any linear independent ...
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1answer
61 views

Linear transformation of vector space - proof of statements

Let $T:V\rightarrow V$ be a linear transformation of vector space with finite dimension. Prove that the following statements are equivalent: $$1. \ \ V=Ker(T) \oplus Im(T) \\ 2. \ \ ...
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2answers
251 views

Combine a rotation matrix with transformation matrix in 3D (column-major style)

I'm trying to concatenate a rotation matrix with a 4x4 homogeneous transformation matrix with column-major convention. I want this rotation matrix to perform a rotation about the X axis (or YZ plane) ...
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2answers
577 views

Consider the trace map $M_n (\mathbb{R}) \to \mathbb{R}$. What is its kernel?

The map is the trace map. I.e, it takes any $n$ by $n$ matrix and associates to that matrix, a number of the form $\mathrm{Tr}(A) = \sum_{i=1}^n a_{ii}$, where $A \in M_n (\mathbb{R})$. I need to ...
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0answers
200 views

How to determine yaw-pitch-roll orientation by specifying a plane via 3 points?

[Note, this question is an attempt at rephrasing the one posted here, as it has not garnered any attention, unfortunately] Hello, Let's say you have three points in 3D space: A, B and C. Together, ...
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1answer
56 views

transformations of $\mathbb R^2$

Consider the transformation $(u,v)=f(x,y)=(x-y,xy)$. Demonstrate the effect of this transformation on the lines $x-y=\text{constant}$, $x+y=0$, and the curves $xy=\text{constant}$. In particular ...
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1answer
224 views

Finding the pre-image of a linear transformation

Let $T$, A linear transformation such that: $$T\left[ {\begin{array}{*{20}{c}} x_1 \\ x_2 \\ x_3 \end{array}} \right] = \left[ \begin{array}{*{20}{c}} 2x_1 - x_2 + 5x_3 \\ - 4x_1 ...
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1answer
112 views

Translating and scaling a line based on two grabbed points

Say there is a line segment going from 0 to 10, now imagine that point 7 and 8 are 'grabbed' and translated to respectively 6 and 11. The effect would this would be that the line segment get's scaled ...
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1answer
38 views

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.