7 projection on a different axes question

In summary, the projection transformation T:R^{2}->R^{2} on the x-axes parallel to the line y=-\sqrt{3}x has a representative matrix of T{*} = \begin{bmatrix}1 & 0 \\ 0 & k\end{bmatrix} with k being determined by trigonometric calculations. This can be found by understanding how the transformation affects the basis B = {(1,0),(0,1)} and using that information to write the representative matrix.
  • #1
415
0
7)
[tex]T:R^{2}->R^{2}[/tex] projection transformation on X-axes parallel to the
line
[tex]y=-\sqrt{3}x[/tex]
find the representative matrices of T{*} by B=\{(1,0),(0,1)\} basis
how i tried:
i understood that the x axes stayed the same but the y axes turned
into
[tex]y=-\sqrt{3}x[/tex]
our T takes some vector and returns only the new x part with respect
to the new y axes.
any guidanse?
 
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  • #2
nhrock3 said:
7)
[tex]T:R^{2}->R^{2}[/tex] projection transformation on X-axes parallel to the
line
[tex]y=-\sqrt{3}x[/tex]
find the representative matrices of T{*} by B=\{(1,0),(0,1)\} basis
how i tried:
i understood that the x axes stayed the same but the y axes turned
into
[tex]y=-\sqrt{3}x[/tex]
our T takes some vector and returns only the new x part with respect
to the new y axes.
any guidanse?

If I understand what you're trying to say, then
[tex]T\begin{bmatrix}1 \\ 0\end{bmatrix} = \begin{bmatrix}1\\ 0\end{bmatrix}[/tex]
and
[tex]T\begin{bmatrix}0 \\ 1\end{bmatrix} = k\begin{bmatrix}1\\\sqrt{3}\end{bmatrix}[/tex]

With a little trig you can figure out what k needs to be. What you know what a linear transformation does to a basis, you can write the matrix that represents the transformation.
 

1. What is meant by "7 projection on a different axes question"?

The phrase "7 projection on a different axes question" refers to a mathematical problem where a 7-dimensional object or set of data is projected onto a different set of axes. This can be done to simplify the problem or to analyze the data from a different perspective.

2. How do you perform a 7 projection on a different axes?

To perform a 7 projection on a different axes, you will need to first determine the new set of axes you wish to project onto. Then, you will use a mathematical technique, such as matrix multiplication or vector calculus, to transform the original 7-dimensional data onto the new axes.

3. What is the purpose of performing a 7 projection on a different axes?

The purpose of performing a 7 projection on a different axes is to simplify the analysis or visualization of complex data. By projecting onto a different set of axes, you can potentially uncover patterns or relationships that were not apparent in the original data.

4. Are there any limitations to 7 projection on a different axes?

Yes, there are limitations to 7 projection on a different axes. One limitation is that some information may be lost in the projection process, particularly if the new axes do not fully capture the complexity of the original data. Additionally, the interpretation of the projected data may be more difficult and may require additional mathematical or statistical techniques.

5. Can 7 projection on a different axes be applied to any type of data?

Yes, 7 projection on a different axes can be applied to any type of data, as long as the data is represented in 7 dimensions. This can include numerical data, geometric shapes, or even abstract concepts. However, the effectiveness of the projection will depend on the nature of the data and the chosen new axes.

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