I have a time-varying random vector, [itex]\underline{m}(t)[/itex], whose elements are unity power and uncorrelated. So, its covariance matrix is equal to the identity matrix.(adsbygoogle = window.adsbygoogle || []).push({});

Now, if I separate [itex]\underline{m}(t)[/itex] into two separate components (a vector and a scalar):

[itex]\underline{m}(t)\triangleq\underline{b}(t)m_0(t)[/itex]

I'm confused as to what I can say about [itex]\underline{b}(t)[/itex] and [itex]m_0(t)[/itex]. In particular, I feel that the covariance matrix of [itex]\underline{b}(t)[/itex] should be proportional to the identity matrix. Therefore, I also feel that [itex]m_0(t)[/itex] should be uncorrelated with the elements of [itex]\underline{b}(t)[/itex]. However, I cannot see how to prove or disprove these things. Where can I start?!

Any help is greatly appreciated!

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

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!

# Simple Covariance Matrix Question

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