All Questions
Tagged with co.combinatorics eigenvector
7 questions
17
votes
2
answers
1k
views
Constructive proof of a rational version of Perron-Frobenius?
In the following, we work with vectors and matrices whose entries are rational numbers. Inequalities between such vectors are understood to be coordinatewise: e.g., two vectors $a = \left(a_1,a_2,\...
- 33.8k
10
votes
2
answers
473
views
Support of eigenvectors
Consider the $N$ by $N$ matrix
$$M_N= \begin{pmatrix} 1+3\lambda & -1-2\lambda & - \lambda & 0 & 0 &0 &0\\
-1-2\lambda & 2+3\lambda & -1 & -\lambda & 0 & 0 &...
- 192
9
votes
1
answer
436
views
Eigenvalues of a matrix with binomial entries
I am trying to determine the eigenvalues and eigenvectors of the following matrix:
$$M_{ij} = 4^{-j}\binom{2j}{i}$$
where it is understood that the binomial coefficient $\binom{m}{k}$ is zero if $k&...
- 884
7
votes
1
answer
254
views
Eigenvectors of a matrix with entries involving combinatorics
In the question Eigenvalues of a matrix with entries involving combinatorics No_way asked about eigenvectors of $n\times n$ matrix $M$ with entries \begin{eqnarray*}
M_{ij}=(-1)^{i+j}F(n, l, i, j),
\...
- 12.3k
1
vote
0
answers
329
views
The geometrical multiplicity of the nilpotent matrices
The following point is well-known in the literature.
Theorem. Let $A$ be a non-negative matrix in $M_n(\mathbb{R})$. If $A$ is nil-potent, there is a permutation matrix $P$ such that $P^tAP$ is ...
- 4,058
1
vote
0
answers
138
views
Relationship betwen eigenvectors
Suppose that we have two matrices A and B. Matrix B is taken from A with one row and one column deleted. On the other hand A is n*n matrix and B is (n-1)*(n-1) matrix and is created by deleting last ...
- 127
0
votes
1
answer
664
views
Kneser graphs eigenvalues
Basically, I want to prove that, in the Kneser graph (wikipedia has a good definition),$K_{n, m}$, if $n_{-}(A(G)) $ and $n_{+}(A(G))$ denote the number of negative and positive eigenvalues of A(G) ...
