- #1
anbhadane
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- TL;DR Summary
- I am reading Jackson's book, where on (p.545) I got some doubts.
In Jackson, (3rd edition p. 545), there are equations they are given as,
$$A = e^L $$
$$det A = det(e^L) = e^{Tr L}$$
$$g\widetilde{A}g = A^{-1} $$
$$ A = e^L , g\widetilde{A}g = e^{{g\widetilde{L}g}} , A^{-1} = e^{-L}$$
$$ g\widetilde{L}g = -L $$
I have several doubts.
1) $$det(e^L) = e^{TrL}$$ How determinant is equal to RHS of equation?, does here are we assuming there is special type of L ?
2) Now in $$ g\widetilde{A}g = e^{{g\widetilde{L}g}}$$, How is it possible to have $$g = e^{g}?$$
$$A = e^L $$
$$det A = det(e^L) = e^{Tr L}$$
$$g\widetilde{A}g = A^{-1} $$
$$ A = e^L , g\widetilde{A}g = e^{{g\widetilde{L}g}} , A^{-1} = e^{-L}$$
$$ g\widetilde{L}g = -L $$
I have several doubts.
1) $$det(e^L) = e^{TrL}$$ How determinant is equal to RHS of equation?, does here are we assuming there is special type of L ?
2) Now in $$ g\widetilde{A}g = e^{{g\widetilde{L}g}}$$, How is it possible to have $$g = e^{g}?$$