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UnkleRhaukus

  • one year 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
    • one year ago
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    If the column matrix is the same as the vector?

  2. UnkleRhaukus
    • one year ago
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    maybe

  3. UnkleRhaukus
    • one year ago
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    i hope so

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

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

  6. klimenkov
    • one year 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
    • one year ago
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    can you explain why that is so ?

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

  9. UnkleRhaukus
    • one year ago
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    yeah,

  10. klimenkov
    • one year 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
    • one year ago
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    do the different vectors fit the same cartesian plane?

  12. klimenkov
    • one year 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
    • one year ago
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    Do you have a concrete example, so I can help you?

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

  16. klimenkov
    • one year 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
    • one year ago
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    http://openstudy.com/study#/updates/50f4096be4b0694eaccfaa5d

  18. klimenkov
    • one year 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
    • one year ago
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    i just made my first 3d template on ti\(k\)z today

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

  21. UnkleRhaukus
    • one year ago
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    * i mean the notation is different

  22. klimenkov
    • one year 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
    • one year 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
    • one year ago
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    Scalar product of the vectors is just a particular case of the general multplication of the matrices.

  25. UnkleRhaukus
    • one year ago
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    can you graph a matrix?

  26. klimenkov
    • one year 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
    • one year ago
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    not even a 2x2 matrix?

  28. klimenkov
    • one year 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
    • one year 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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