I've learned that a vector in coordinate system can be expressed as follows:(adsbygoogle = window.adsbygoogle || []).push({});

A=aA_{x}_{x}+aA_{y}_{y}+aA_{z}_{z}.

a, i = x, y, z, are the base vectors._{i}

The transformation matrix from cylindrical coordinates to cartesian coordiantes is:

A_{x}cosΦ -sinΦ 0 A_{r}

A_{y}= sinΦ cosΦ 0 mutiplye by A_{Φ}

A_{z}0 0 1 A_{z}

and the conversion formula

x = rcosΦ

y = rsinΦ

z = z

Thanks in advance.

- What's the difference between this two kind of equations?
- Why A
_{x}is not equal to x?- I was told that A
_{x}might be a function of x, y and z. Is the latter kind of equaltions has a prerequisite that a_{x}= (1, 0, 0), but in the first kind of equations, the base vector can be anything else?- From the matrix, A
_{x}= cosΦA_{r}- sinΦA_{Φ}, that is not equal to x = rcosΦ !? Why? How should I apply the transformation matrix?

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# Transform Cylindrical coordinates into Cartesian Coordiantes

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