# stochastic processes: variance of a random variable obtained from a linear transformation

Edit: I needed to review this question as suggested.

Suppose there are $$N$$ Realizations of the Gaussian process denoted as vectors $$mathbf {z} _ {j} in mathbb {R} ^ {n}$$ for $$j = 1, ldots, N$$. Leave $$and$$ be a random variable such that $$y = sum_ {j = 1} ^ {N} ( mathbf {B} mathbf {z} _ {j}) (i)$$
where $$mathbf {B}$$ It is a unitary matrix. What is the variance of $$y2$$?

Explanation: Boldface represents the vector or matrix. $$( mathbf {B} mathbf {x}) (i)$$ represents the $$i$$-th vector entry $$mathbf {B} mathbf {x}$$.