There are three very common tags related to matrix decomposition/factorization, namely diagonalization, svd and jordan normal form.
I've seen some questions related to other matrix decompositions, namely $QR$ decomposition, Cholesky decomposition, Schur decomposition and $LU$ decomposition.
I would like to create a tag called matrix decomposition and have it included as synonyms the following terms: matrix factorization, $LU$ decomposition, $LU$ factorization, $QR$ decomposition, $QR$ factorization, Cholesky decomposition, Cholesky factorization, Schur decomposition, Schur factorization and triangularization.
I would like input on wether to include diagonalization, svd and jordan normal form in the synonym list above.
Side questions: do the tags need to exist for it to be possible to be included as synonyms? If there is no question tagged $LU$ decomposition, is it possible to include $LU$ decomposition as a synonym? If it isn't possible, why not allow us such prophylactic measures?