Do any of the linear algebra gurus here know the name of or a citation for the following paired matrix decomposition: given symmetric matrices `A`

and `B`

, and an arbitrary vector `v`

, find a decomposition of the form

```
A = W DA W'
B = W DB W'
```

for real matrices `W`

satisfying `W' v = [1,1,...,1]`

and `DA`

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, Iād rather acknowledge & call it by name.