- #1
Yossi
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Homework Statement
Let K and L be symmetric PSD matrices of size N*N, with all entries in [0,1]. Let i be any number in 1...N and K’, L’ be two new symmetric PSD matrices, each with only row i and column i different from K and L. I would like to obtain an upper bound of the equation below: where .∗ is an element-wise multiply.
Homework Equations
|[sum(K' .∗ L') − sum(K .∗ L)] − (2/N)*[sum(K'L'') − sum(KL)] + (1/N*N)*[sum(K')sum(L') − sum(K)sum(L)]|
See attached for equation in LaTex/PDF.
The Attempt at a Solution
Using simple triangular inequality and bounding the three square brackets respectively,
I can bound the above with 12N − 13.
However, this is extremely loose.
Empirical experiments show that the constant coefficient should be much lower, probably closer to 1N.
Can you suggest any linear algebra properties connecting the equation's parts - which may help me get a tighter bound?