Index notation
Does anyone know how to demonstrate this identity?
Let $\displaystyle D=det(a_{ij})$
$\displaystyle \epsilon_{ijk}\epsilon_{pqr}D=
\begin{vmatrix}
a_{ip} & a_{iq} & a_{ir} \\
a_{jp} & a_{jq} & a_{jr} \\
a_{kp} & a_{kq} & a_{kr}
\end{vmatrix}
$
The book demonstrates this way: "If (at least) two of i, j, k or two of p, q, r are equal, then both sides of (1.7.21) are 0. If i, j, k and p, q, r are both cyclic or acyclic, then each side of (1.7.21) is equal to D. If i, j, k are cyclic but p, q, r are acyclic or vice versa, then each side of (1.7.21) is equal to D. Thus, in all possible cases, result (1.7.21) is verified."
But for me it doesn't make sense, this sum would give 0.
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Work on:
General thermal systems
Cryogenics
Microdrop fluid mechanics
