Recent questions in Matrix transformations

Matrix transformations
Answered

oxidricasbt7
2022-12-20

I have no idea where to begin.

I know there are a few matrices that support this claim, will they all have the same eigenvalues?

Matrix transformations
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Jayden Davidson
2022-12-18

Matrix transformations
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e3r2a1cakCh7
2022-12-03

$XA=B,X={A}^{-1}B$

Matrix transformations
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atgnybo4fq
2022-11-12

$A=\left(\begin{array}{ccc}1& 2& 4\\ 3& 6& 5\end{array}\right)$

Matrix transformations
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Hugo Stokes
2022-10-18

Matrix transformations
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Paloma Sanford
2022-10-13

Is $b$ in the range of linear transformation $x\to Ax$?

Matrix transformations
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Krish Schmitt
2022-09-30

Now consider the ${n}^{2}$ dim vector space $V\u2a02V$ (kronecker product) with equivalent basis sets $\{{s}_{1}{s}_{1},{s}_{1}{s}_{2},...,{s}_{n}{s}_{n}\}$ and $\{{e}_{1}{e}_{1},{e}_{1}{e}_{2},...,{e}_{n}{e}_{n}\}$. Now can we find the basis transformation matrix for this in terms of U?

Matrix transformations
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Chelsea Lamb
2022-09-26

Matrix transformations
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Julia Chang
2022-09-25

Matrix transformations
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Colten Andrade
2022-09-21

$$\frac{1}{m}}{\mathrm{\Theta}}^{T}{Y}^{T}Y\mathrm{\Theta}={I}_{p\times p},$$

where 𝐼𝑝×𝑝 is identity matrix.

My attempt: $\frac{1}{\sqrt{m}}}Y\mathrm{\Theta$ is orthogonal matrix and tried to find $\mathrm{\Theta}$ satisfies it but that doesn't work.

Matrix transformations
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Celinamg8
2022-09-20

$$\begin{array}{r}\left[\begin{array}{c}0\\ \vdots \\ 0\\ ||u||\end{array}\right]=Qu.\end{array}$$

Matrix transformations
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nar6jetaime86
2022-09-13

$T\phantom{\rule{mediummathspace}{0ex}}:\phantom{\rule{mediummathspace}{0ex}}R2\left(x\right)\phantom{\rule{mediummathspace}{0ex}}->R2\left(x\right)\phantom{\rule{mediummathspace}{0ex}}defined\phantom{\rule{mediummathspace}{0ex}}by\phantom{\rule{mediummathspace}{0ex}}T(a{x}^{2}+bx+c)=2ax+b$

Matrix transformations
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tamola7f
2022-09-13

Matrix transformations
Answered

Julius Blankenship
2022-09-12

Let $||T||=inf\{M\ge 0:||T(x)||\le M||x||\text{}\mathrm{\forall}x\in {\mathbb{K}}^{n}\}$ be the operator norm of a linear transformation $T:{\mathbb{K}}^{n}\to {\mathbb{K}}^{m}$.

Show that the operator norm of the linear transformation $T$ is also given by:

$$||T||=max\{\sum _{i=1}^{m}|{a}_{ij}|,1\le j\le n\}=:||A|{|}_{1}$$

where $A$ is the transformation matrix of $T$ and ${a}_{ij}$ it's entry in the $i$-th row and $j$-the column.

Matrix transformations
Answered

tuzkutimonq4
2022-09-11

$$\left[\begin{array}{cccccccc}0& 0& 1& 1& 0& 0& 1& 1\\ 0& 0& 0& 0& 1& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]$$

To the following:

$$\left[\begin{array}{cccccccc}0& 0& 1& 1& 0& 0& 1& 1\\ 0& 0& 0& 0& 1& 1& 1& 1\\ 0& 1& 0& 1& 0& 1& 0& 1\end{array}\right]$$

Matrix transformations
Answered

engausidarb
2022-09-11

If you are dealing with linear algebra, the chances are high that you will encounter various questions related to matrix transformation. Turning to matrix transformation examples, you will also encounter various geometric transformations, yet these will always be based on algebraic analysis and calculations. The answers that we have presented to various challenges will help you to compare our solutions with your unique matrix transformation example that deals with linear transformation and mapping. Visual assistance is also included and will be essential to see how these are built with the help of the column vectors.