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Jan 4, 2015 at 22:44 history closed DanielSank
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Jan 4, 2015 at 22:38 comment added DanielSank This is pure math question with absolutely no physical context.
Jan 4, 2015 at 22:36 history edited JamalS CC BY-SA 3.0
edited body
Sep 16, 2014 at 20:06 comment added Valter Moretti @Danu Sorry, I am presently too busy with lectures and other things to read and comment that question :c
Sep 16, 2014 at 16:32 vote accept LorentzNoether
Sep 16, 2014 at 8:39 comment added MSalters "Linear Algebra is linear". In the end, it's that simple. The multiplication is just a basis transform. Physical reality does not change by your arbitrary choice of a basis, so the (differential) equations describing reality should hold up in any basis.
Sep 16, 2014 at 0:11 answer added doetoe timeline score: 5
Sep 15, 2014 at 22:45 answer added ACuriousMind timeline score: 12
Sep 15, 2014 at 21:36 comment added Valter Moretti If $A$ is not a normal matrix it cannot be diagonalized that way. Instead $^T$ has to be replaced by $^{-1}$. However, in general $A$ is not diagonalizable and its determinant is not the product of its eigenvalues...
Sep 15, 2014 at 21:27 history edited Qmechanic CC BY-SA 3.0
deleted 11 characters in body; edited tags; edited title
Sep 15, 2014 at 21:21 comment added Andrew McAddams You may diagonalize $\hat{A}$: $\hat{A} = \hat{U}\hat{A}{'}\hat{U}^{T}$, where $det U = 1 , \hat{A}{'} = diag (A_{1}, ...)$. Then $det A = det U det A{'}det U^{T} = det A{'}$.
Sep 15, 2014 at 21:21 comment added higgsss The Jacobian determinant! Actually it should be absolute value $|{\rm det} A|$
Sep 15, 2014 at 21:02 history asked LorentzNoether CC BY-SA 3.0