# I'm already tr(r)

I shall begin by saying that I thought about this today in my Detection and Estimation Class while looking at the mse calculations for the MMSE estimator.

Let’s suppose we have a vector of discrete s of elements with the following rule:

which means

Suppose we are given a square matrix .

A square matrix has the operator **Trace** () defined
as the sum of the elements on its main diagonal:

Suppose that the value is part of the set of values that can assume.

Now suppose that the variable assumes the value of . Indeed:

So is **Trace(R)**.

Let’s now suppose that also another random variable , with wants to assume the role of **Trace(R)**.

However,

Therefore, the variable cannot assume the value of **Trace(R)** and should proceed to choose another value, since is already **Trace(R)**.

Sorry about this stupid meme.