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Results tagged with eigenvalues
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user 502666
eigenvalues of matrices or operators
1
vote
2
answers
369
views
Eigenvectors of a non-symmetric rank-one update of a symmetric matrix
I have a matrix $A$ $(n\times n)$ with eigenvalues $\lambda_i$, then I add another matrix to it as: $A+uv^\top$ where $u$ $(n\times 1)$ and $v$ $(n\times 1)$ are column vector. … Is there any way to calculate the new eigenvalues and eigenvectors of $(uv^\top+yy^\top)$ using the information from the vector $u$,$v$ and the eigenvalues and eigenvectors of $yy^\top$？ …
- 63
0
votes
0
answers
73
views
Approximate solution problem of rank-one modification matrix secular equation
I get the first $k$ terms of new eigenvalues $\lambda_j$? … \end{equation*}
Is there any way that we can calculate the new eigenvalues $\lambda$? and how to choose which sets of $uj$ and $dj$ to solve for the eigenvalues? …
- 63
4
votes
1
answer
2k
views
Eigenvalues of a rank-one update of a symmetric matrix
I have a matrix $A$ $(n\times n)$ with eigenvalues $\lambda_i$, then I add another matrix to it as: $A+xx^\top$ where $x$ $(n\times 1)$ is a column vector.
and also $A=yy^\top$ with $y$ a $(n-1)$ rank … Is there any way to calculate the new eigenvalues and eigenvectors of $(xx^\top+yy^\top)$ using the information from the vector $x$ and the eigenvalues and eigenvectors of $yy^\top$？ …
- 63