Robert Mansel Gower

3 Questions 9 Answers 0 Followers

Questions related from Robert Mansel Gower

How to calculate the covariance of a standard normal random vector projected onto the sphere?

Given x ~ N(0,I) is an n-dimensional normal random vector, where I is the identity matrix. Prove that E [ x x^T / (x^Tx)] = (1/n) I, Or equivalently, let y = x/||x||, what is the covariance of y ?

13 April 2015 7,131 3 View

What is the covariance of a normalized random vector?

Given x ~ N(0,D) is an n-dimensional normal random vector, where D is a diagonal matrix with positive entries. Prove that $E [ x x^T / (x^Tx)] = D^(1/2) / trace(D^(1/2))$, Or equivalently, let y =...

12 April 2015 9,471 3 View

Functions and Hilbert spaces. What would you call the inner product between an element in the domain and its corresponding image under a function?

Let f: \R^n -> \R^n be a function. What would you call the function g: x -> x' f(x) ? Furthermore, if F:\R^n -> \R^n is a linear operator and D \in \R^{n X m} a matrix, how would you...

29 November 2014 9,245 3 View