A linear transformation x_1^, | = | a_11 x_1 + a_12 x_2 + a_13 x_3 x_2^, | = | a_21 x_1 + a_22 x_2 + a_23 x_3 x_3^, | = | a_31 x_1 + a_32 x_2 + a_33 x_3, is said to be an orthogonal transformation if it satisfies the orthogonality condition a_(i j) a_(i k) = δ_(j k), where Einstein summation has been used and δ_(i j) is the Kronecker delta.
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