name for a matrix decomposition $T^{-1} S T$ (S lower and T upper triangular)

Question

A given real square matrix $M$ has a decomposition

$M = T^{-1} S T$

where $S$ and $T$ are lower and resp. upper triangular with '$1$'s in the diagonal. Does this type of decomposition have a known classification/name? I could not find something similar under the wikipedia entry for matrix decomposition.

Thank you