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RZA Chris
RZA Chris
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I was wondering what we can say about the eigenvectors of a matrix $A$ fullfilling $Ax =0$ where $A$ is symmetric with a diagonal equal to one and every row sums up to 0. Obviously this is a generalisation of the graph Laplacian with positiv weights. It s easy to see that the constant vector is an Eigenvector to 0. I m not sure if there are more. Any help or pointers would be greatly appreciated.

Edit: the underlying graph is connected

I was wondering what we can say about the eigenvectors of a matrix $A$ fullfilling $Ax =0$ where $A$ is symmetric with a diagonal equal to one and every row sums up to 0. Obviously this is a generalisation of the graph Laplacian with positiv weights. It s easy to see that the constant vector is an Eigenvector to 0. I m not sure if there are more. Any help or pointers would be greatly appreciated

I was wondering what we can say about the eigenvectors of a matrix $A$ fullfilling $Ax =0$ where $A$ is symmetric with a diagonal equal to one and every row sums up to 0. Obviously this is a generalisation of the graph Laplacian with positiv weights. It s easy to see that the constant vector is an Eigenvector to 0. I m not sure if there are more. Any help or pointers would be greatly appreciated.

Edit: the underlying graph is connected

Source Link
RZA Chris
RZA Chris
  • 1
  • 1

Eigenvector to zero eigenvalue of general Laplacian

I was wondering what we can say about the eigenvectors of a matrix $A$ fullfilling $Ax =0$ where $A$ is symmetric with a diagonal equal to one and every row sums up to 0. Obviously this is a generalisation of the graph Laplacian with positiv weights. It s easy to see that the constant vector is an Eigenvector to 0. I m not sure if there are more. Any help or pointers would be greatly appreciated