The matrix giving the relation between spherical (unit) vectors and cartesian (unit) vectors can be expressed as:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\left( \begin{array}{c} \hat{r} \\ \hat{\phi} \\ \hat{\theta} \end{array} \right) =

\left( \begin{array}{ccc} \sin\theta \cos\phi & \sin\theta \sin\phi & \cos\theta \\ -\sin\phi & \cos \phi & 0 \\ \cos\theta \cos\phi & \cos\theta \sin\phi & -\sin\theta \end{array}\right) \cdot \left( \begin{array}{c} \hat{x} \\ \hat{y} \\ \hat{z} \end{array} \right) [/tex]

or

[tex]T = \left( \begin{array}{ccc} \sin\theta \cos\phi & \sin\theta \sin\phi & \cos\theta \\ -\sin\phi & \cos \phi & 0 \\ \cos\theta \cos\phi & \cos\theta \sin\phi & -\sin\theta \end{array}\right) [/tex]

where phi is the polar angle and theta is the azimuthal angle.

Can this matrix T be factored into simpler matrices?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Matrix Factorization

Loading...

Similar Threads for Matrix Factorization |
---|

I Eigenproblem for non-normal matrix |

A Eigenvalues and matrix entries |

A Badly Scaled Problem |

I Adding a matrix and a scalar. |

B How does matrix non-commutivity relate to eigenvectors? |

**Physics Forums | Science Articles, Homework Help, Discussion**