TITLE: Linear algebra problem related to the Kalman filter
QUESTION [1 upvotes]: I'm studying a special case of the Kalman filter, and the following problem has come up:
Suppose $H \in R^{d\times 1}$, and $R$ is a positive definite $d \times d$ matrix. How would I show that
$H^\top ( H H^\top + R)^{-1} H $ lies between 0 and 1?
Presumably there's an easy fact about matrix norms that I'm missing, but what's the right way to handle this expression?

REPLY [1 votes]: In case anyone else ever encounters this problem, one can solve it using the Sherman-Morrison formula.
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