The discussion revolves around finding the expected value of the L2 norm of the expression ||Ax+n||, where x and n are uncorrelated random variables and the expected value of n is zero. The participants are examining the implications of this setup in the context of linear algebra and probability.
The discussion is active, with participants clarifying each other's expressions and exploring the simplifications of the expected value. There is a focus on ensuring the mathematical validity of their manipulations, but no consensus has been reached on further simplification.
Participants are working under the assumption that x and n are uncorrelated and that E[n] = 0, which influences their reasoning about the terms in the expected value calculation.
You mean E[x'A'Ax +x'A'n +n'Ax +n'n] , right?cutesteph said:E[ norm of Y] = E[(Ax+n)' (Ax+n)] = E[(x'A'+n')(Ax+n)] = E[x'A'xA +x'T'n +n'Ax +n'n]
x'A'Ax is a scalar; x'A'x is a scalar; (x'A'x)A is an n x n matrix; x'(A'xA) is meaningless (since xA is meaningless).cutesteph said:Yes. But the result is still the same since it is a scalar