The least squares estimate correctly weighted by !:. -1 is x = (AT!:. -1 A) -1 AT!:. -1
Chapter 8, Problem 8(choose chapter or problem)
The least squares estimate correctly weighted by !:. -1 is x = (AT!:. -1 A) -1 AT!:. -1 b. Call that x = Lb. If b contains an error vector e , then x contains the error Le. The covariance matrix of those output errors Le is their expected value (average value) P = E [(Le)(Le)T] = LE [eeT] LT = L!:.LT. Problem: Do the multiplication L!:.LT to show that P equals (AT!:.-l A)-I as predicted in equation (10).
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