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I have a matrix in LDLT $X=LDL^T$ form, where all nonzero elements in L (i.e. diagonal and below), are $1$. So only D matters (which is diagonal). What can we tell about the eigenvalues/vectors of this matrix?

It is possible to assume for simplicity that $X$ is positive definite, i.e. D's diagonal is all positive.

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    We can assume full rank and all positive eigenvalues, i.e. we can assume $X$ is symmetric and positive definite. Also,$L$is invertible in our case. The problem is that its vectors are only independent, not orthogonal. But as expected I need the eigenvalues themselves, not their count. Thanks!!!2012-12-08

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