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
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