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Lie brackets are bi-linear so whatever you do per example automatically carries over to sums, the bracket for the batch is just the pairwise brackets for elemen
by measurablefunc 6mo ago
Lie brackets are bi-linear so whatever you do per example automatically carries over to sums, the bracket for the batch is just the pairwise brackets for elements in the batch, i.e. {a + b + c, d} = {a, d} + {b, d} + {c, d}. Similarly for the second component.
- thaumasiotes 6mo ago> Similarly for the second component. Hmm. {a + b, c + d} = {a, c + d} + {b, c + d} = {a, c} + {a, d} + {b, c} + {b, d}. {a + b + c, x + y + z} = {a, x + y + z} + {b, x + y + z} + {c, x + y + z} = (a sum of nine direct brackets). This doesn't look like it will scale well.
- measurablefunc 6mo agoThen don't use the Lie bracket. All bilinear forms scale the same way.