2008-07-30, 11:10 PM
Okay, I'm studying the kronecker delta and the alternating tensor. (As in e[123] = e[231] = e[312] = 1, e[321] = e[132] = e[213] = -1, e[ijk] = 0 otherwise).
I have to prove that e[ijk]e[rsk] = δ[ir]δ[js] - δ[is]δ[jr] using the identity (This is gonna be hard to write
e[ijk]e[rst] =
| δ[ir] δ[is] δ[it] |
| δ[jr] δ[js] δ[jt] |
| δ[kr] δ[ks] δ[kt] |
But every time I go through it, I wind up with the signs backwards, ie e[ijk]e[rsk] = δ[is]δ[jr] - δ[ir]δ[js]
Anyone have any idea what I might be doing wrong?
I have to prove that e[ijk]e[rsk] = δ[ir]δ[js] - δ[is]δ[jr] using the identity (This is gonna be hard to write
e[ijk]e[rst] =
| δ[ir] δ[is] δ[it] |
| δ[jr] δ[js] δ[jt] |
| δ[kr] δ[ks] δ[kt] |
But every time I go through it, I wind up with the signs backwards, ie e[ijk]e[rsk] = δ[is]δ[jr] - δ[ir]δ[js]
Anyone have any idea what I might be doing wrong?