0
votes
0answers
28 views

Reversible smoothing of a two dimensional function (or an image)

Smoothing of an image, or a two dimensional function is quite easy, there are many methods to achieve it, using average of near elements. But how to make it reversible? Maybe DCT (discrete cosine ...
0
votes
1answer
32 views

What is the difference between a bijection and a reversible transformation?

I was reading http://arxiv.org/abs/quant-ph/0101012v4 and one of the axioms is that there needs to be a continuous reversible transformation between states. What is the difference between that and a ...
1
vote
3answers
30 views

Find that the given linear transform is a isomorphism

I'm studying Linear Algebra and I'm having trouble demonstrating that a function is a isomorphism, that is: "Given the linear transform $T: V \rightarrow W$, $T$ is a isomorphism if and only if it is ...
-1
votes
1answer
29 views

Understanding a definition for vector-spaces

Let $V$, a finite dimensional vector space, and $L$, a subspace of $V$. Let $T:V^*\rightarrow L^*$ defined as: $T(\varphi)(x)=\varphi(x)$ for all $\varphi \in V^*$. Prove $T$ is onto. Well, I'm ...
1
vote
1answer
21 views

$\ker S$ is not contained in $\ker T$ implies $\dim \Im T \ge 1$

Let $T,S:V\rightarrow W$.where $V$ is a finite vector space above $F$ and $W$ is one-dimensional vector-space above $F$ ($\dim W = 1$). It is given that $\ker S$ isn't contained in $\ker T$. Why is ...
1
vote
0answers
15 views

Existence of a particular transformation

I've a set of data points $S = \{ x | x\in [0,1]\}$ (i.e. real values from the unit interval). In some cases I've big clusters in the data and I want to spread the values in between the unit interval ...
0
votes
2answers
30 views

Function tranlsation $g(x) = f(x) + 15$

I can't seem to work this answer out when practicing for exams. Here's the question: You are given that $f(x) = (2x - 3)(x + 2)(x + 4) \cdots$ From this I know $f(x)$'s roots: $\frac{3}{2}$, ...
1
vote
1answer
32 views

Function inverse mapping [0, +inf) to [0, 1)

I have a measure ($x$) which the domain is $[0, +\infty)$ and measure some sort of variability. I want to create a new measure ($y$) that represents regularity and is inverse related to $x$. It is ...
0
votes
1answer
49 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} ...
0
votes
1answer
14 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.
1
vote
1answer
48 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?
3
votes
1answer
74 views

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 ...
4
votes
1answer
2k views

“Well defined” function - What does it mean?

What does it mean for a function to be well-defined? I encountered with this term in an excersice asking to check if a linear transformation is well-defined.
0
votes
1answer
40 views

What's the difference between these two transformations of functions?

I'm about to graph the transformation of a function, but in this problem I encountered something new. The function transformation looks like this: y=12(f(x)+2) Thing is, I've never seen the f ...
2
votes
2answers
277 views

Find the matrix A of the linear transformation T(M)

I know that if I substitute the first matrix for $T(M)$ I see what T does to each of the basis vectors. I don't understand how that creates a $3\times 3$ matrix though. I was looking at this ...
2
votes
0answers
42 views

Bijection from the plane to itself that takes a circle to a circle must take a straight line to a straight line

Prove, that a bijection from the plane to itself that takes a circle to a circle must take a straight line to a straight line. There exists an elementary proof? I know this question can be found here ...
2
votes
2answers
67 views

What does the notation f(t)1(t) signify?

I've come across this notation in a text on Control Theory, Modern Control Engineering by Katsuhiko Ogata, in a discussion of Laplace transforms. There is little more context I can give than that. ...
1
vote
1answer
69 views

Distribution of the Inverse of a Random Variable

I am trying to figure out how to find the distribution of the inverse of a random variable. Say, $Y=X^{-1}$ where X can take negative values. The two ways I know to find the distribution of a random ...
4
votes
3answers
322 views

Image of function definition notation

In my Linear Algebra and Geometry textbook, it defines the image of a linear transformation $T$ as: $$\operatorname{Im}\, (T) := \{\; w \in W : \; w=Tv \;\;\text{ for some } v \in V \} $$ As far as ...
0
votes
2answers
74 views

Number mapping function

I can't find out a function f(x)=y that would map my x's to required y's. It is OK to write it in a programming language. Notation in mathematics is also OK. It ...
1
vote
0answers
17 views

Need help transforming an list of numbers into some uniform list in order to apply the rule mentioned inside more effectively

So I have a list of values like so L1 = [-4 -3 5 8 ]; Note the sum of each element in L1 will always be > 0. The operation I am performing on L1 is as follows ...
2
votes
1answer
156 views

Reflecting an exponential function over a y = 3 line.

How would you write the equation of $f(x) = 4^x$ that reflects over the line $y = 3$? I've put in $f(x) = 3 + 4^{-x}$ which I thought was the right answer, but it isn't. Thanks in advance!
1
vote
1answer
51 views

Coordinate transformation to get even function

Suppose I have the function $$f(y)=2y^4-5y^3+3y^2,$$ with zeroes $y=0$ (2x), $y=1$, $y=3/2$, which I only need on the part of the domain $0\le y\le 1$. Is there a transformation $y\rightarrow y'$, ...
0
votes
1answer
2k views

Function transformation order of operations

I am reviewing for a midterm for Pre-Calculus and I am trying to understand the concept of function transformation: Let's say I am given a function $f$ with the domain in the interval of $[1,5]$ and ...
1
vote
1answer
330 views

Translating Cubic with Algebra?

I'm having a little trouble figuring out how to translate $ax^3+bx^2+cx+d=y$ by vector $(1,1)$ using only algebra. If possible could someone give me a hand? An example: Translate ...
1
vote
1answer
50 views

Trouble with function transformation (Left and right)

I am reading this example in the book for Pre-Calculus and it is explaining how functions are shifted left or right using g(x)=f(x-1). Here is what it says in the book. Define a function g by g(x) = ...
4
votes
1answer
127 views

Can a transformation matrix be expressed in terms of the vector to be transformed?

I'm currently learning linear algebra with my friend via an online course, and we have a disagreement that we would like settled. Upon learning that vectors can be projected onto lines by a simple ...
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 ...
1
vote
0answers
117 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 ...
1
vote
2answers
137 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 $\alpha=1$ ...