A relation between Laplacians
$begingroup$
I'm currently working on the following problem, that consists in establishing conditions (if any) for the existence of two weighted Laplacian matrices that verify a given relation. I make the following distinction for sake of clarity. I will refer to a
- Laplacian to indicate a positive semi-definite Laplacian matrix
- Loopy Laplacian to indicate a strictly positive definite Laplacian matrix
Let $Linmathbb{R}^{ntimes n}$ a Laplacian matrix and $Pinmathbb{R}^{ntimes n}$, $Qinmathbb{R}^{ntimes n}$ two diagonal positive definite matrices.
Determine, if possible, conditions on A, P, Q so that
$$
L'=PL(mathbb{I}_n+QL)^{-1}.
$$
is
1) a Laplacian
2) a loopy Laplacian
matrix-calculus graph-laplacian
asked Jan 14 at 12:39
DanieleDaniele
12
$endgroup$
add a comment |
$begingroup$
I'm currently working on the following problem, that consists in establishing conditions (if any) for the existence of two weighted Laplacian matrices that verify a given relation. I make the following distinction for sake of clarity. I will refer to a
- Laplacian to indicate a positive semi-definite Laplacian matrix
- Loopy Laplacian to indicate a strictly positive definite Laplacian matrix
Let $Linmathbb{R}^{ntimes n}$ a Laplacian matrix and $Pinmathbb{R}^{ntimes n}$, $Qinmathbb{R}^{ntimes n}$ two diagonal positive definite matrices.
Determine, if possible, conditions on A, P, Q so that
$$
L'=PL(mathbb{I}_n+QL)^{-1}.
$$
is
1) a Laplacian
2) a loopy Laplacian
matrix-calculus graph-laplacian
asked Jan 14 at 12:39
DanieleDaniele
12
$endgroup$
add a comment |
$begingroup$
I'm currently working on the following problem, that consists in establishing conditions (if any) for the existence of two weighted Laplacian matrices that verify a given relation. I make the following distinction for sake of clarity. I will refer to a
- Laplacian to indicate a positive semi-definite Laplacian matrix
- Loopy Laplacian to indicate a strictly positive definite Laplacian matrix
Let $Linmathbb{R}^{ntimes n}$ a Laplacian matrix and $Pinmathbb{R}^{ntimes n}$, $Qinmathbb{R}^{ntimes n}$ two diagonal positive definite matrices.
Determine, if possible, conditions on A, P, Q so that
$$
L'=PL(mathbb{I}_n+QL)^{-1}.
$$
is
1) a Laplacian
2) a loopy Laplacian
matrix-calculus graph-laplacian
asked Jan 14 at 12:39
DanieleDaniele
12
$endgroup$
I'm currently working on the following problem, that consists in establishing conditions (if any) for the existence of two weighted Laplacian matrices that verify a given relation. I make the following distinction for sake of clarity. I will refer to a
- Laplacian to indicate a positive semi-definite Laplacian matrix
- Loopy Laplacian to indicate a strictly positive definite Laplacian matrix
Let $Linmathbb{R}^{ntimes n}$ a Laplacian matrix and $Pinmathbb{R}^{ntimes n}$, $Qinmathbb{R}^{ntimes n}$ two diagonal positive definite matrices.
Determine, if possible, conditions on A, P, Q so that
$$
L'=PL(mathbb{I}_n+QL)^{-1}.
$$
is
1) a Laplacian
2) a loopy Laplacian
matrix-calculus graph-laplacian
matrix-calculus graph-laplacian
asked Jan 14 at 12:39
DanieleDaniele
12
asked Jan 14 at 12:39
DanieleDaniele
12
edited Jan 14 at 13:05
Daniele
asked Jan 14 at 12:39
DanieleDaniele
12
asked Jan 14 at 12:39
DanieleDaniele
12
asked Jan 14 at 12:39
DanieleDaniele
12
12
add a comment |
add a comment |
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