Hi everyone.(adsbygoogle = window.adsbygoogle || []).push({});

There is the ##2\times 2## matrix ##B##

$$B=

\left[

\begin{array}{cc}

B_{11} &B_{12} \\

B_{21}&B_{22}

\end{array}

\right],~B_{ij}\in \mathbb{C}

$$

with property

$$\vert B_{11}\vert^2 + \vert B_{12}\vert^2=1,$$

$$\vert B_{21}\vert^2 + \vert B_{22}\vert^2=1,$$

$$B_{11}B_{21}^{\ast}+B_{12}B_{22}^{\ast}=0.$$

According to one of the texts, it is said that this matrix can be decomposed like

$$B=e^{i\frac{\Lambda}{2}}

\left[

\begin{array}{cc}

e^{i\frac{\Phi}{2}} & 0 \\

0 & e^{-i\frac{\Phi}{2}}

\end{array}

\right]

\left[

\begin{array}{cc}

\cos (\Theta/2) & \sin (\Theta/2) \\

-\sin (\Theta/2) & \cos (\Theta/2)

\end{array}

\right]

\left[

\begin{array}{cc}

e^{i\frac{\Psi}{2}} & 0 \\

0 & e^{-i\frac{\Psi}{2}}

\end{array}

\right]

$$

$$\Lambda, \Phi, \Theta, \Psi \in \mathbb{R}$$.

I don't know what kind of decomposition this is.

Could someone tell me the name of this decomposition?

Thanks.

**Physics Forums - The Fusion of Science and Community**

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!

# I Decomposition of Matrix

Tags:

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Decomposition Matrix | Date |
---|---|

I Conics -- Matrix Decomposition | May 18, 2017 |

QR Decomposition w/ Householder and Givens Transformations | Mar 1, 2015 |

Question on decomposition of a matrix | Apr 8, 2014 |

Decomposition of matrix | Nov 30, 2013 |

Matrix Diagonalization & Eigen Decomposition | Nov 11, 2013 |

**Physics Forums - The Fusion of Science and Community**