jessicata comments on Matrices map between biproducts

[jessicata]

I believe bra/​ket is for row and column vectors. I don’t think it applies here, because in the general case (semiadditive categories), you have arbitrary linear maps as the $h_{j,i}$ entries. And in the $R^m\to R^n$ case, they’re reals, not row or column vectors.

It is true that you can decompose as either $⟨[\dots ]\dots [\dots ]⟩$ or $[⟨\dots ⟩\dots ⟨\dots ⟩]$. To be clear I’m using $⟨⟩$ and [] from category theory product/​coproduct notation, it’s not meant to match linear algebra or bra/​ket notation.