Timeline for Why is not ${(\Lambda^T)^\mu}_\nu = {\Lambda_\nu}^\mu$?

9 events

when toggle format	what		by	license	comment
Aug 22, 2017 at 16:06	history	edited	Qmechanic♦		edited tags
Apr 30, 2017 at 17:52	vote	accept	Mikkel Rev
Apr 30, 2017 at 9:51	history	edited	Qmechanic♦	CC BY-SA 3.0	added 3 characters in body
Apr 30, 2017 at 9:50	answer	added	Qmechanic♦		timeline score: 12
Apr 29, 2017 at 23:21	comment	added	Mikkel Rev		@knzhou By your first comment, I believe you confirm that you're puzzled too, correct? Flipping the indecies is exactly what I propose, but that's what the lecture notes do not.
Apr 29, 2017 at 23:09	comment	added	knzhou		The upstairs/downstairs index placement is a red herring that can only add confusion; it's not a 'real' index because $\Lambda$ is not a tensor.
Apr 29, 2017 at 23:08	comment	added	knzhou		I think you're put an extra flip in there somewhere. Just think about it like matrices: $ABC = D$ means $A_{ij} B_{jk} C_{k\ell} = D_{i\ell}$. Therefore $A^T BC = D$ means $B_{jk} A_{ji} C_{k\ell} = D_{i\ell}$ where I used the commutativity of multiplication, and replaced $A_{ij}$ with $A_{ji}$. This is exactly the same as equation (1).
Apr 29, 2017 at 22:31	history	edited	Qmechanic♦	CC BY-SA 3.0	edited tags
Apr 29, 2017 at 22:18	history	asked	Mikkel Rev	CC BY-SA 3.0