I have an [itex](m \times n)[/itex] complex matrix, [itex]\textbf{N}[/itex], whose elements are zero-mean random variables. I have a sort of covariance expression:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\mathcal{E}\left\{\textbf{N}\textbf{N}^H\right\} = \textbf{I}[/itex]

where [itex]\mathcal{E}\left\{\right\}[/itex] denotes expectation, [itex]\{\}^H[/itex] is conjugate transpose and [itex]\textbf{I}[/itex] is the identity matrix.

Basically, I want to know exactly what this tells me about the second order statistics of the elements of [itex]\textbf{N}[/itex]. For example, I know that if instead I just had an [itex](m \times 1)[/itex] vector, [itex]\textbf{n}[/itex], then an identity covariance matrix would imply that all the elements of [itex]\textbf{n}[/itex] have unit variance and are uncorrelated.

Can I make any similar deductions from the matrix equation, above? Many thanks for any help!

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

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!

# Covariance matrix of 2 matrices?

Loading...

Similar Threads - Covariance matrix matrices | Date |
---|---|

A Covariance matrix for transformed variables | Sep 30, 2016 |

I Covariance in fitting function | Jun 12, 2016 |

Covariance matrix with asymmetric uncertainties | Oct 20, 2015 |

Valid Covariance Matrices | Nov 30, 2014 |

Covariance matrix does not always exist? | Dec 13, 2013 |

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