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UnkleRhaukus

  • 2 years ago

\[\newcommand\ve[1]{\vec{\boldsymbol #1}} % vector \newcommand\uv[1]{\hat{\boldsymbol #1}} % unit vector \begin{equation*}\ve A=\begin{bmatrix}a_1\\a_2\\a_3\end{bmatrix}=\langle a_1,a_2,a_3\rangle\\ \end{equation*}\]?

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  1. PeterPan
    • 2 years ago
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    If the column matrix is the same as the vector?

  2. UnkleRhaukus
    • 2 years ago
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    maybe

  3. UnkleRhaukus
    • 2 years ago
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    i hope so

  4. PeterPan
    • 2 years ago
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    I don't understand the question (if this is a question) :(

  5. UnkleRhaukus
    • 2 years ago
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    well i'm trying to understand the different notations,,

  6. klimenkov
    • 2 years ago
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    It depends on the situation. In one case you can use different notations for the vector and in another - you cant.

  7. UnkleRhaukus
    • 2 years ago
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    can you explain why that is so ?

  8. klimenkov
    • 2 years ago
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    Yes, I can. Do you know anything about matrix multiplication?

  9. UnkleRhaukus
    • 2 years ago
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    yeah,

  10. klimenkov
    • 2 years ago
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    So I show a case, when the row notation and the column notation should not be confused. Lets take two vectors: \(\vec{a}=\left(\begin{matrix}1\\2\end{matrix}\right)\) and \(\vec{b}=(3,4)\). And now multiply \(\vec{a}\) on \(\vec{b}\), and then \(\vec{b}\) on \(\vec{a}\): \(\vec{a}\vec{b}=\left(\begin{matrix}1\\2\end{matrix}\right)(3,4)=\left(\begin{matrix}3&4\\6&8\end{matrix}\right)\) \(\vec{b}\vec{a}=(3,4)\left(\begin{matrix}1\\2\end{matrix}\right)=3\cdot1+4\cdot2=11\) If we confuse the rows and the columns we will have the wrong result, because it is important to know where is the column and where is the row. But in other case, when we say about a vector in general, without multiplication, it is not so important to know if it is a row or a column.

  11. UnkleRhaukus
    • 2 years ago
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    do the different vectors fit the same cartesian plane?

  12. klimenkov
    • 2 years ago
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    2D vectors can represent the points of the cartesian plane. So the different vectors represent different points. And they fit this plane.

  13. klimenkov
    • 2 years ago
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    Do you have a concrete example, so I can help you?

  14. UnkleRhaukus
    • 2 years ago
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  15. UnkleRhaukus
    • 2 years ago
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    or should one of those be on the z axis?

  16. klimenkov
    • 2 years ago
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    It is ok. Why do you think any of those must be on z-axis? One more question: how did you draw this pic?

  17. UnkleRhaukus
    • 2 years ago
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    http://openstudy.com/study#/updates/50f4096be4b0694eaccfaa5d

  18. klimenkov
    • 2 years ago
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    Oh. I thought about it, but it is too long to draw pics in TikZ. Or you have good skills?

  19. UnkleRhaukus
    • 2 years ago
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    i just made my first 3d template on ti\(k\)z today

  20. UnkleRhaukus
    • 2 years ago
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    i suppose i think the different vectors look different, so they must be orthogonal somehow

  21. UnkleRhaukus
    • 2 years ago
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    * i mean the notation is different

  22. klimenkov
    • 2 years ago
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    No. Different vectors on the plane are the vectors, that has different components. The notation doesn't play any role.

  23. UnkleRhaukus
    • 2 years ago
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    ok so then, the operation of multiplying the vectors somehow chooses that the first vector to be a row vector for dot product, right?

  24. klimenkov
    • 2 years ago
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    Scalar product of the vectors is just a particular case of the general multplication of the matrices.

  25. UnkleRhaukus
    • 2 years ago
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    can you graph a matrix?

  26. klimenkov
    • 2 years ago
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    You have to know what a matrix interprete. It is a table of numbers. My answer is No.

  27. UnkleRhaukus
    • 2 years ago
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    not even a 2x2 matrix?

  28. klimenkov
    • 2 years ago
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    No. How do you think, what does this matrix will show on the plane? A components of the vectors can be read as the point, but what is a matrix?

  29. berlingots
    • 2 years ago
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    since you written an arrow on top of the A, I assume it is a vector. So the vector is 3 dimensional in R^3. Let the a's equal x, y, and z standing for its components. The second is written in column form and the last one is written in row form. I hope this answers your question. They are both equal but written differently notation wise.

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