5 ms·
I remember when I was learning matrix calculus and realized at some point that it was much simpler to convert everything to index notation, perform all operatio
by Xcelerate 8y ago
I remember when I was learning matrix calculus and realized at some point that it was much simpler to convert everything to index notation, perform all operations, then convert everything back to standard notation at the end. It became almost comically simple, because you're "just" working with labeled scalars at that point. To be fair, it's convenient to memorize some of the more commonly used expressions (like ∂tr(AB)/∂B) rather than rederive them from scratch.
- krastanov 8y agoRoger Penrose (the famous mathematician) has been saying the same thing for a couple of decades (going even further than that, check out Penrose diagrams).
- jesuslop 8y agoAnd Penrose diagrams (tensor networks) became a prominent example of String Diagram in the monoidal category of vector spaces over a field.
- cdavid 8y agoI am interested: do you have a reference that shows this through examples ? In my grad school years, I was always dissatisfied by matrix calculus notations
- cdavid 8y agoInteresting, I almost always got the exact opposite experience. How do you calculate non trivial matrix derivatives using index notation ?
- mcabbott 8y agoYou insert kronecker deltas: ∂M_ab / ∂M_cd = δ_ac δ_bd , and a,b here remain contracted with whatever M was originally contracted with. Then you simplify, δ_ac Z_xya = Z_xyc and so on.