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## Homework Statement:

- Prove that Tr(αA+βB) = αTr(A)+βTr(B). α and β are complex constants, and A and B are dXd matrices

## Relevant Equations:

- Tr(αA+βB) = αTr(A)+βTr(B)

First, i'd like to apologize for the vague title. Unfortunately my understanding of the question is equally vague. I think the dXd matrix is meant to be a covariance matrix, so the above equation would be some complex constant multiplied by the covariance matrix. The Tr would referring to the trace of the matrix or sum of diagonal elements. So i'm attempting to show that the "trace of the sum A+B" is equal to "trace A + trace B".

Here's my main problem. I have never heard of a covarience matrix before. If someone could show me a simple example of what a covarience matrix is then I should be able to figure out the additive, multiplicative, etc... rules of these matrices.

Here's my main problem. I have never heard of a covarience matrix before. If someone could show me a simple example of what a covarience matrix is then I should be able to figure out the additive, multiplicative, etc... rules of these matrices.