indepotent and symmetric matrix


New member
Sep 11, 2019
Hello :) I've been working myself through a problemset, but I am now stuck at this excercise. I dont understand what they mean by the first info, is i just a column with the number 1 downwards? Many thanks in advance for any help.

In the following, let i be an N-dimensional column vector with 1s. For some N-dimensional column vector y, the average value of the components in y is given by

(1/N) i' y.

Let I be the identity matrix with dimension N × N. Consider the matrix

M0 = I − (1/N) i i'

The matrix M0 is idempotent. That the matrix is idempotent means that M0M0 = M0

d) Show that
1. M0 is symmetric.
2. M0 is idempotent.

- Ben