## UnkleRhaukus 2 years ago $\newcommand\ve[1]{\vec{\boldsymbol #1}} % vector \newcommand\uv[1]{\hat{\boldsymbol #1}} % unit vector \begin{equation*}\ve A=\begin{bmatrix}a_1\\a_2\\a_3\end{bmatrix}=\langle a_1,a_2,a_3\rangle\\ \end{equation*}$?

1. PeterPan

If the column matrix is the same as the vector?

2. UnkleRhaukus

maybe

3. UnkleRhaukus

i hope so

4. PeterPan

I don't understand the question (if this is a question) :(

5. UnkleRhaukus

well i'm trying to understand the different notations,,

6. klimenkov

It depends on the situation. In one case you can use different notations for the vector and in another - you cant.

7. UnkleRhaukus

can you explain why that is so ?

8. klimenkov

Yes, I can. Do you know anything about matrix multiplication?

9. UnkleRhaukus

yeah,

10. klimenkov

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

do the different vectors fit the same cartesian plane?

12. klimenkov

2D vectors can represent the points of the cartesian plane. So the different vectors represent different points. And they fit this plane.

13. klimenkov

Do you have a concrete example, so I can help you?

14. UnkleRhaukus

15. UnkleRhaukus

or should one of those be on the z axis?

16. klimenkov

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
18. klimenkov

Oh. I thought about it, but it is too long to draw pics in TikZ. Or you have good skills?

19. UnkleRhaukus

i just made my first 3d template on ti$$k$$z today

20. UnkleRhaukus

i suppose i think the different vectors look different, so they must be orthogonal somehow

21. UnkleRhaukus

* i mean the notation is different

22. klimenkov

No. Different vectors on the plane are the vectors, that has different components. The notation doesn't play any role.

23. UnkleRhaukus

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

Scalar product of the vectors is just a particular case of the general multplication of the matrices.

25. UnkleRhaukus

can you graph a matrix?

26. klimenkov

You have to know what a matrix interprete. It is a table of numbers. My answer is No.

27. UnkleRhaukus

not even a 2x2 matrix?

28. klimenkov

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

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.