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32 views

Lanczos algorithm with thick restart on a dynamic matrix

currently, I'm working on a way to compute the 2 biggest eigenvalues of a real, symmetric, huge and sparse matrix that changes a few entries from time to time. The problem should be solved using an ...
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Eigenvalue of (0-1) matrix

Assume I have 2 matrices, each of size nxn with only 1 and 0 as entries in both. (n>10) The first matrix (call it A) has each row summing up to 2 (ie: on each row, it has two "1" and n-2 "0"). It is ...
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Eigenvalues of a “Half-Kronecker ” Product

The Problem: Given a 2 by 2 matrix $C$(the matrix elements of C are given), and two other 2 by 2 matrices $A$ and $B$(the matrix elements of A and B are given). Now we can construct a new matrix ...
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Relationship of eigenvalue/eigenvector of hermitian matrix R and QRQ (Q is diagonal)

For a hermitian matrix R and a diagonal one Q, is there any relationship between eigenvalues/eigenvectors of R and QRQ? To be specific, assuming the eigenvalue decomposition of R is R=VDV*, then can ...
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When is this matrix singular?

Consider matrix $A$ with $(j,k)$â€˛th entry $A_{j,k}=\sin(\omega_j t_k+\phi_j),\,\forall j,k\in\{1,2,...,n\}$, where $\omega_j,t_k,\phi_j\in \mathbf R$. 1) For $t_k=k$, what is the condition on ...
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Which graph topology has the greatest eigenvalue?

I am looking at comparing multiple graph topologies based on their spectra. From the set of all $N\times N$ adjacency matrices, is there any result which points to the adjacency matrix with the ...
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Epidemic threshold

Need some help / ideas to proceed. Stuck for a while on this. In the literature of epidemic theory, it is found that the epidemic threshold is $1/\lambda_{max}(A)$ where $\lambda_{max}(A)$ is the ...
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Eigenvalues of permutations of a real matrix: how complex can they be?

This is sort of complementary to this thread. Iâ€™ll repeat the definitions here: For a matrix $M\in GL(n,\mathbb R)$, consider the $n!$ matrices obtained by permutations of the rows (say) of $M$ and ...
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Eigenvalues of permutations of a real matrix: can they all be real?

For a matrix $M\in GL(n,\mathbb R)$, consider the $n!$ matrices obtained by permutations of the rows (say) of $M$ and define the total spectrum $TS(M)$ as the union of all their spectra (counting ...
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Upper bounds on eigenvalues of PSD matrix?

Suppose A is a symmetric positive semidefinite matrix. Is there a way to upper bound the largest eigenvalue using properties of its row sums or column sums? For instance, the Perronâ€“Frobenius ...