
• This Question is Open
1. PeterPan Group Title

If the column matrix is the same as the vector?

2. UnkleRhaukus Group Title

maybe

3. UnkleRhaukus Group Title

i hope so

4. PeterPan Group Title

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

5. UnkleRhaukus Group Title

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

6. klimenkov Group Title

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

7. UnkleRhaukus Group Title

can you explain why that is so ?

8. klimenkov Group Title

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

9. UnkleRhaukus Group Title

yeah,

10. klimenkov Group Title

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 Group Title

do the different vectors fit the same cartesian plane?

12. klimenkov Group Title

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

13. klimenkov Group Title

14. UnkleRhaukus Group Title

15. UnkleRhaukus Group Title

or should one of those be on the z axis?

16. klimenkov Group Title

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 Group Title
18. klimenkov Group Title

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

19. UnkleRhaukus Group Title

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

20. UnkleRhaukus Group Title

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

21. UnkleRhaukus Group Title

* i mean the notation is different

22. klimenkov Group Title

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

23. UnkleRhaukus Group Title

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 Group Title

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

25. UnkleRhaukus Group Title

can you graph a matrix?

26. klimenkov Group Title

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

27. UnkleRhaukus Group Title

not even a 2x2 matrix?

28. klimenkov Group Title

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 Group Title

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.