Do any of the linear algebra gurus here know the name of or a citation for the following paired matrix decomposition: given symmetric matrices
B, and an arbitrary vector
v, find a decomposition of the form
A = W DA W' B = W DB W'
for real matrices
W' v = [1,1,...,1] and
DB block-diagonal with 1x1 or 2x2 blocks.
W is not required to be orthonormal.
I can probably figure out how to compute this myself (it seems very close to the generalized eigendecomposition), but if it already exists, I’d rather acknowledge & call it by name.