- #1
vishnu vardha
- 1
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ε
show that the determinant of a matrix A can be calculated as followings:
det[A]= 1/6 (A_ii A_jj A_kk + 2 A_ij A_jk A_ki - 3 A_ij A_ji A_kk
use ε_pqr det[A]= ε_ijk A_ip A_jq A_kr
ε_pqr ε_pqr det[A]= ε_ijk ε_pqr A_ip A_jq A_kr
use ε_pqr ε_pqr = 6
det[A]= 1/6 ( ε_ijk ε_pqr A_ip A_jq A_kr)
and ε_ijk ε_pqr = det | δ_ip δ_iq δ_ir |
| δ_jp δ_jq δ_jr |
| δ_kp δ_kq δ_kr |
from here i don't know what to do
and δ - delta and ε - epsilon
Homework Statement
show that the determinant of a matrix A can be calculated as followings:
det[A]= 1/6 (A_ii A_jj A_kk + 2 A_ij A_jk A_ki - 3 A_ij A_ji A_kk
Homework Equations
The Attempt at a Solution
use ε_pqr det[A]= ε_ijk A_ip A_jq A_kr
ε_pqr ε_pqr det[A]= ε_ijk ε_pqr A_ip A_jq A_kr
use ε_pqr ε_pqr = 6
det[A]= 1/6 ( ε_ijk ε_pqr A_ip A_jq A_kr)
and ε_ijk ε_pqr = det | δ_ip δ_iq δ_ir |
| δ_jp δ_jq δ_jr |
| δ_kp δ_kq δ_kr |
from here i don't know what to do
and δ - delta and ε - epsilon