this is a proof I encounter in William Greene econometric analysis appendix section.
If A is a n*k with full column rank and n > k, then (A')(A)is positive definite and (A)(A') is positive semi-definite.
proof given by author is as follows,
By assumption, Ax is not equal to zero. So, x'A'Ax = (Ax)'(Ax) = y'y = summation y^2 > 0
for the latter case, because A has more rows then columns, then there is an X such that A'x = 0, thus we can only have y'y >= 0
What I dont understand is the the bold and underline part.
P/S: this question comes from pg 835, of William Greene Econometric Analysis 5th edition textbook.
Thanks in Advance !!!