new postfix transpose() operator different from '

[johnalx]

Can we introduce a new postfix operator for the transpose, like A^⊤ or A̕ ?

It would of great help to us who write expressions with a lot of transposes. For example:

a = (transpose(s)*A*s)\s*(Q-transpose(s)*p+U*transpose(R)*κ)

and it would more true to form if the multiple calls to transpose() were replaced with something more terse. Even if the language defaulted to transpose for A' unless it knew a complex data type was used when the adoint is more appropriate.

[MasonProtter]

Ref #34507, #21037

If you like, you can always do this:

struct Transposer end
const ᵀ = Transposer() #typed \^T<TAB>
Base.:(*)(x, ::Transposer) = transpose(x)

julia> rand(5)ᵀ*randn(5,5)*rand(5)
0.7409506780313673

julia> A = rand(5); (A)ᵀ*rand(5, 5)*A
2.7952114562233827

[johnalx]

Ref #34507, #21037

If you like, you can always do this:

struct Transposer end
const ᵀ = Transposer() #typed \^T<TAB>
Base.:(*)(x, ::Transposer) = transpose(x)

julia> rand(5)ᵀ*randn(5,5)*rand(5)
0.7409506780313673

julia> A = rand(5); (A)ᵀ*rand(5, 5)*A
2.7952114562233827

Yet the following does not work

z = rand(3)
zᵀ*z    # ERROR: UndefVarError: zᵀ not defined

And that is the point of having a built in operator, such that the parser will recognize zᵀ as transpose(z). This hack is interesting, though.

[MasonProtter]

It works if you surround z in parentheses.

julia> (z)ᵀ*z
1.4221674642522308

I should also reference this PR: #34549 where they run PkgEval to show what registered packages would be effected by changing the meaning of zᵀ from just a variable named zᵀ to transpose(z). The list of broken packages is quite small, but the Julia devs take breaking changes very seriously.

[JeffBezanson]

duplicate of #21037

[JeffBezanson]

Even if the language defaulted to transpose for A' unless it knew a complex data type was used when the adoint is more appropriate.

Isn't that already the case --- adjoint and transpose are equivalent for reals?