# 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), (rigid-...

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### Transformation of coordinate axis to make matrix diagonal

Consider the matrix $$A= \begin{bmatrix}1/8 & \frac{-5}{8\sqrt{3}} \\ \frac{-5}{8\sqrt{3}} & 11/8 \end{bmatrix}$$ which of the following transformations of the coordinate ...
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### How to prove that a bijective transformation is NOT continuous

I am having this transformation $f: \mathbb R \to \mathbb R$ $$f(x) = \begin{cases} x & x \in \mathbb R \setminus \mathbb Q \\x+1 & x \in \mathbb Q \end{cases}$$ I've already prooved ...
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### Prove: the sum of simultaneously diagonalizable transformations is diagonalizable

Let $T, S$, linear transformations which are simultaneously diagonalizable. Prove that $T+S$ is diagonalizable. I need to rely on the the definition: $T,S$ are called simultaneously diagonalizable ...
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### Is $f: [0,1[ \cup \{ 2 \} \to [0,1]$ continuous?

I am having this transformation $f: [0,1[ \cup \{ 2 \} \to [0,1]$ $$f(x) = \begin{cases} x & x \neq 2 \\1 & x = 2 \end{cases}$$ How can I prove that this transformation is continuous or ...
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### No continuous transformation $f([a,b])= ]a,b[$

$a,b\in\mathbb R$ with $a<b$. Now I want to show that there is NO continuous transformation $f: [a,b] \to \mathbb R$ with $f([a,b])= ]a,b[$ How can I proove that this transformation don't ...
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### Problem of Closed linear transformation in Normed spaces [duplicate]

Let $X$ a normed space and let $A$ and $B$ be linear transformations such that $$X\subset D_A\rightarrow^{A} X \ \ \text{and} \ \ X\subset D_B\rightarrow^{B} X.$$ If $A$ and $B$ are closed, does it ...
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### M22 → R Matrix Transformation Kernel

For a transformation such as this, how does one determine the form of the kernel? Is it simply making the right side equal to zero, solving for each individual variable, and then creating a matrix ...
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### $p(x)$ divides the minimal polynomial iff $\exists v\ne 0: p(T)(v)=0$

Let $V$, a finite dimensional space. Let $T:V\to V$ a linear transformation. Show that $p(x)$, an irreducible polynomial divides $m_T$ (The minimal polynomial of $T$) iff there is a $V\ni v \ne 0$ ...
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### Can anyone help me with “rotation matrix” and “Image of matrix”?

If A is a 3 by 3 matrix which gives a rotation about some line through the origin in R^3 , then columns of A form a basis of R^3 For any matrix A, the image of A^7 is contained in the image of A Every ...
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### Transforming 1D Burger's Equation into infinitely many coupled ODE's

I've been working on the following problem but I can't justify my steps, would a savvy mathematician kindly tell me what, if any, violations I've made. Problem: Show Burger's equation can be written ...
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### Express a 90 degree rotation matrix in terms of a 180 degree rotation matrix? (both anti-clockwise)

A = [-1 0 0 ] [ 0-1 0 ] [ 0 0 1 ] B = [0 -1 0 ] [ 1 0 0 ] [ 0 0 1 ] How can i represent B in terms of A?
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### How do I detect if a 4x4 transformation matrix contains reflection?

We currently check if the determinant of the upper left 3x3 values is negative to detect reflection in a 4x4 transformation matrix but we are unsure that it works in all cases (any arbitrary 3D ...
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### Can anyone explain relationship between “onto” and “columns are independent” ?

I remember reading this statement before. It is as follows. Transformation is onto if and only if columns are linearly independnet Transformation is one-to-one if and only if rows are independent ...
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### Find a matrix representing a given linear transformation [duplicate]

$T(X) = [\{x_1-x_2+x_3\}, \{0+x_2-x_3\}, \{0+0+0\}]$ is a linear transformation from $\mathbb R^3$ to $\mathbb R^3$. Find a matrix $A$ such that $T(x) = A(x)$ Can anyone point me in the right ...
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### what is the difference between linear transformation and affine transformation?

Recently, I am struglling with the difference between linear transformation and affine transformation. Are they the same ? I found an interesting question on the difference between the functions. But ...
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### Easy little triangle configuration

One of the four shapes is not needed to make the shape in the first pic. Which one? Once again, is it just noticing some properties? Or are there any other logical ways of figuring it out? I ...
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### Proving: $\exists n\le \dim_F(V):V=\Im (T^n)\oplus \ker(T^n)$

Let $V$ above $\mathbb{F}$ and let $T:V\to V$. Prove there is a $n\le \dim_\mathbb{F} V$ such that $V=\Im(T^n)\oplus \ker(T^n)$ Now I know that for all $k$: $\ker (T^{k}) \subseteq \ker(T^{k+1})$ ...
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### Can There Be A Dilation That Maps Parallelogram B to Parallelogram A?

There are 2 parallelograms, A and B. They have the same angle measures. Both have 2 sides that measure 6 units. Parallelogram As 2nd set of parallel lines are longer than the 2nd set of parallelogram ...