Let’s look at the six three-by-three permutation matrices. We can label them by how they permute the rows. We have P_{123} equal to the identity matrix. P_{231} has the second row of the identity
The Remarkable Relationship between the Levi-Civita Symbol and the Kronecker Delta | Deep Dive Maths
Though with speed and velocity values still interleaved, we continue to use shuffling of sorts, though now that's done by the `permute` instruction. Our familiar multiply and add instructions have also combined into a fused-multiply-and-add, further improving performance.
4x Code Performance with SIMD