By assumptions (i)-(ii), Z X is qp of rank p, and Z Z is qq of rank
Question:
By assumptions (i)-(ii), Z
X is q×p of rank p, and Z
Z is q×q of rank q. Show that:
(a) Z
Z is positive definite and invertible; the inverse has a square root.
(b) X
Z(Z
Z)−1Z
X is positive definite, hence invertible. Hint. Suppose c is p×1. Can c
X
Z(Z
Z)−1Z
Xc ≤ 0?
Note. Without assumptions (i)-(ii), equations (10) and (13) wouldn’t make sense.
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