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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

1 vote
0 answers
3k views

Is adding an outer product to a matrix guaranteed to not decrease the eigenvalues? [closed]

Given a symmetric matrix $A$ and a vector $v$, will adding $v v^T$ to $A$ always increase or keep the eigenvalues of $A$ the same? The sum of the eigenvectors of $A + v v^T$ should be greater or equal …