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5
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0answers
211 views

concentration for eigenvectors

I am interested in bounding from above the ratio between the maximum and minimum entries of a Perron vector. The only results that I found in the literature are from the classic masters (Ostrowski and ...
0
votes
0answers
182 views

How to understand the matrix behind a Hamiltonian?

thanks to the answers I received to my previous questions, I could derive correctly an elegant partition function for my problem which resembles a second quantized model taking the particles to be ...
12
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2answers
1k views

Determinants in Graph Theory

In graph theory, we work with adjacency matrices which define the connections between the vertices. These matrices have various properties in themselves. For example, their trace can be calculated (it ...
2
votes
0answers
394 views

eigenvalues of a symmetric tridiagonal matrix with zero diagonals

I was investigating a problem and came up with the following symmetric tridiagonal matrix (with zero diagonal elements): $$ \left(\begin{array}{cccccc} 0 & a & 0 & \ldots & 0 \\ a ...
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vote
1answer
1k views

Cholesky decomposition of a positive semi-definite

We know that a positive definite can be done for Cholesky decomposition,but I want to know that how a positive semi-definite be done for Cholesky decomposition?The following sentences come from a ...