# OrePolynomialMatrixOperations(F, LO)ΒΆ

- F: Field
- LO: UnivariateSkewPolynomialCategory F

undocumented

- rowEchelon: (Matrix LO, F, List Vector F) -> Record(mat: Matrix LO, vecs: List Vector F)
`rowEchelon(m, c, lv)`

returns [`m2`

,`lv2`

] such that`m2`

is the row echelon form of the matrix`m`

.`lv2`

is transformed`lv`

using`c`

as paramenter to`apply`

.

- solve: (Matrix LO, F, List Vector F, (LO, List F) -> Record(particular: List Record(ratpart: F, coeffs: Vector F), basis: List F)) -> Union(Record(particular: List Record(ratpart: Vector F, coeffs: Vector F), basis: List Vector F), failed)
`solve(m, c, lv, solf)`

returns “failed” of [[`vp1`

, ..., vp_m], [`b1`

, ...,`bl`

]] such that`bi`

-`s`

are basis of solutions of homogeneous system`m`

`bi`

= 0. Each vpi = [`r`

, [`c1`

, ...,`cn`

]] is a particuar solution of a parametic matrix equation`m`

`r`

= sum`ci`

`vi`

where`lv`

= [`v1`

, ...,`vn`

]. solf is scalar solver,`c`

is a paramenter to`apply`

(needed for astion of LO on`F`

). “failed” means that system is underdetermined.