Linear Algebra and Its Applications · Problem 3.3.28

Orthogonality — Gilbert Strang

Mathematics · statistics-unbiased-estimate

Problem

First assumption behind least squares: Each measurement error has mean zero. Multiply the 8 error vectors b−Ax=(±1,±1,±1)b - Ax = (\pm 1, \pm 1, \pm 1) by (ATA)−1AT(A^T A)^{-1} A^T to show that the 8 vectors x^−x\hat{x} - x also average to zero. The estimate x^\hat{x} is unbiased.

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