coeffs

[blegat]

First, I wanted to ask whether it can be renamed coefficients like it's done in MultivariatePolynomials.
But actually, I'd like to also apply the inverse, adjoint, etc... of this map.
For instance, if I have a bridge that converts a vector from one basis to the other one then the dual of that bridge will need to apply the adjoint.
Getting the ConstraintPrimal will need to apply the inverse and setting ConstraintDualStart will need to apply the inverse of the adjoint.
Maybe we could have

struct BasisChange{C,T,S} <: AbstractMatrix{C} # From Source to Target
    target::T
    source::S
end

and then coeffs becomes

Base.:*(::BasisChange, coeffs)

and coeffs! becomes

MA.operate_to!(dest, ::typeof(*), ::BasisChange, coeffs)

and we'll also have

MA.operate_to!(dest, ::typeof(*), ::Adjoint{BasisChange}, coeffs)

etc...
The change of basis of a matrix can also be

Base.:*(::BasisChange, ::Matrix, ::BasisChange)

[kalmarek]

absolutely!

[blegat]

transformation_matrix(dest, src), maybe using LinearMap.jl.