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I also noticed a small mistake in the PR that added LinearAlgebra.svd support. For a matrix, svd returns U, S as a vector, V as the adjoint of a matrix (Vᴴ). So I guess we want to replicate this, and thus have something like

U, S, Vᴴ = svd_compact(t) # or svd_full
return U, diagview(S), adjoint(Vᴴ)

Maybe you can also include this in the current PR?

Added a small fix to address @Jutho's comment (hopefully)

I'm slightly worried that the diagview will fail for the full case, since we don't return a diagonal in that case. LinearAlgebra actually outputs things that don't multiply correctly there, and I'm not sure how we want to handle this?

I guess this is why we didn't overload the linearalgebra methods 😂

I'm slightly worried that the diagview will fail for the full case, since we don't return a diagonal in that case. LinearAlgebra actually outputs things that don't multiply correctly there, and I'm not sure how we want to handle this?

Should I just add a test for full and see what happens?

Alternatively: is anyone actually using these overloads? Can we just remove them, for now?

I'm happy to remove them again, definitely is independent of this PR

Since they don't seem to be tested anyway I say kill em all!!!

Nightly failures are the same Zygote stuff as usual. Is this good to go?