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## Main Question or Discussion Point

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.

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!

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!