# Tagged Questions

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), ...

45 views

### Linear Algebra Dimension

Let $L(U,V)$ = $\{T:U\rightarrow V\ :\ T\ \text{linear}\},$ and dim $(U)=n$, dim $(V)=m$. Then show that $$\dim L(U,V) = mn.$$ I don't know how to begin and I already searched the internet to find ...
108 views

256 views

### Find invariant points, how to express using parameter

I have a matrix $$\begin{pmatrix}0&-1\\1&2\end{pmatrix}$$ where I have to find the invariant points for a transformation using this matrix. I have no problem working through to two ...
88 views

69 views

### Transformation Matrix project

My task is to find the Transformation Matrix, that projects, any point of the xy-plane, on the line $$y = 4x$$ The solution should be: $$T=\pmatrix{0.06&0.235\\0.235&0.94}$$ But somehow i ...
61 views

### How to find an unitary transformation of $A$ that minimize $(A'_{i,i}-1)^2$?

Is there a way to find an unitary transformation $$A'=U^+AU$$ that minimize: $$(A'_{i,i}-1)^2$$ In other words, the diagonal elements must be similar to one: $A'_{i,i} \approx 1$ Any hint? ...
74 views

### Linear transformation

Let there be a linear transformation $T:R^3\rightarrow R^2$ Is there a linear transformation so that: $Ker(T)=Span((1,2,1),(0,3,-1))$ and $Im(T)=Span((5,-7))$ Answer: $Dim(V)=Rank(T)+Null(T)=2+1=3$ ...
104 views

### Why does the discrete cosine transform compact the information at the “low frequencies”?

I've been investigating about the discrete cosine transform. I think I understand the practical applications it has and how it is used in image/audio compression. I also know it is related with the ...
66 views

### How do you prove a hilbert transform?

I am stuck with this question below, I need help;
1k views

39 views

### Finding transformation function for a distribution that looks like exponential

Suppose that we have two data sets, R and P. R is larger than or equal to ...
64 views

63 views

### Halmos Measure Theory section 39 Theorem D

I have trouble explaining the remark "The function $\phi$ plays the role of Jacobian (or, rather, the absolute value of the Jacobian) in the theory of transformation of multiple integrals". I know ...
167 views

### Why would the discrete fourier transform “see” signals like this? What is the origin of spectral leakage?

The discrete fourier transform of $x = (x_{0},\dots,x_{N-1})$ is defined as $\displaystyle X_{k} = \sum_{n=0}^{N-1} x_{n}\omega^{kn}_{N}$ where $\omega^{kn}_{N} = e^{-2\pi ik/N}$ and ...
75 views

### Mobius transformations are bijections proof

I don't understand the last line of this proof. To show a function is bijective we need to show it is one-to-one and onto. The proof shows that $f$ is one-to-one only. For some reason $f^{-1}$ ...
125 views

### Given the minimal polynomial, find the largest invariant subspace

Let the linear transformation T on the vector space $V$ over $\mathbb{Q}$ have minimal polynomial $(x^{7} - x^{3})$. a) What is the largest invariant subspace W of V for which $T (W) = W$? b) Find a ...
43 views

### Changing the length scale of the system of coordinates

Change the length scale on the axes of original system of coordinates, in which the equation $$y=x^3-px\qquad\text{(1)}$$ is plotted, i.e. introduce new coordinates $x_1$ and $y_1$ instead of ...
63 views

### Do rotations of one point around all arbitrary axes form a sphere?

Correct me if I am wrong but assume I have a point in 3D which I would like to rotate around all arbitrary axes fixed at common origin. Then this is true that all orbits circled by rotated point will ...
33 views

### Strongest 'average' for a diverse set of numbers?

I have a set of numbers consisting of two general size numbers: size 'a', and size 'b' which are about three times bigger in size than size 'a'. There is some variation and the list might look like ...