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If we write P_{ijk} P^T_{lmn}, and do the matrix multiplication in the usual way of multiplying rows against columns, we can make use of the orthonormality of the e vectors to get P_{ijk} P^T_{lmn} equals this Kronecker delta
The Remarkable Relationship between the Levi-Civita Symbol and the Kronecker Delta | Deep Dive Maths
If we write P_{ijk} P^T_{lmn}, and do the matrix multiplication in the usual way of multiplying rows against columns, we can make use of the orthonormality of the e vectors to get P_{ijk} P^T_{lmn} equals this Kronecker delta
The Remarkable Relationship between the Levi-Civita Symbol and the Kronecker Delta | Deep Dive Maths