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?

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# Matrix Factorization

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