Sherman-Morrison formula for non-invertible bmatrices
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I am trying to find an expression for inverse of the following matrix
$(L+frac1nJ)$
Where $L$ is the Laplacian of a simple, connected graph with $n$ vertices and $m$ edges, and $J=11^T$ is the all $1$ matrix. It is known that $L$ is singular, while the above matrix is non-singular. Does there exist some formula akin to ShermanâÂÂMorrison formula for this kind of inverse computation?
linear-algebra matrices pseudoinverse graph-laplacian
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up vote
2
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I am trying to find an expression for inverse of the following matrix
$(L+frac1nJ)$
Where $L$ is the Laplacian of a simple, connected graph with $n$ vertices and $m$ edges, and $J=11^T$ is the all $1$ matrix. It is known that $L$ is singular, while the above matrix is non-singular. Does there exist some formula akin to ShermanâÂÂMorrison formula for this kind of inverse computation?
linear-algebra matrices pseudoinverse graph-laplacian
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I am trying to find an expression for inverse of the following matrix
$(L+frac1nJ)$
Where $L$ is the Laplacian of a simple, connected graph with $n$ vertices and $m$ edges, and $J=11^T$ is the all $1$ matrix. It is known that $L$ is singular, while the above matrix is non-singular. Does there exist some formula akin to ShermanâÂÂMorrison formula for this kind of inverse computation?
linear-algebra matrices pseudoinverse graph-laplacian
I am trying to find an expression for inverse of the following matrix
$(L+frac1nJ)$
Where $L$ is the Laplacian of a simple, connected graph with $n$ vertices and $m$ edges, and $J=11^T$ is the all $1$ matrix. It is known that $L$ is singular, while the above matrix is non-singular. Does there exist some formula akin to ShermanâÂÂMorrison formula for this kind of inverse computation?
linear-algebra matrices pseudoinverse graph-laplacian
edited Aug 26 at 20:26
Omnomnomnom
122k784170
122k784170
asked Jan 26 at 21:23
Sudipta Roy
1708
1708
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