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UnkleRhaukus

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

  • one year ago
  • one year ago

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  1. PeterPan
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    If the column matrix is the same as the vector?

    • one year ago
  2. UnkleRhaukus
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    maybe

    • one year ago
  3. UnkleRhaukus
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    i hope so

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

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

    • one year ago
  6. klimenkov
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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.

    • one year ago
  7. UnkleRhaukus
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    can you explain why that is so ?

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

    • one year ago
  9. UnkleRhaukus
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    yeah,

    • one year ago
  10. klimenkov
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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.

    • one year ago
  11. UnkleRhaukus
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    do the different vectors fit the same cartesian plane?

    • one year ago
  12. klimenkov
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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.

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

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

    • one year ago
  16. klimenkov
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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?

    • one year ago
  17. UnkleRhaukus
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    http://openstudy.com/study#/updates/50f4096be4b0694eaccfaa5d

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

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

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

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

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

    • one year ago
  23. UnkleRhaukus
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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?

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

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

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

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

    • one year ago
  28. klimenkov
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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?

    • one year ago
  29. berlingots
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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.

    • one year ago
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