Lagrange's identity is the algebraic identity
(Mitrinovic 1970, p. 41). In determinant form,
where
is the determinant of . Lagrange's identity is a special case of the Binet-Cauchy identity, and Cauchy's inequality in n dimensions follows from it. It can be coded in Mathematica as follow.
Plugging in gives the n = 2 and n = 3 identities
(1)
(Mitrinovic 1970, p. 41). In determinant form,
(2)
where
is the determinant of . Lagrange's identity is a special case of the Binet-Cauchy identity, and Cauchy's inequality in n dimensions follows from it. It can be coded in Mathematica as follow. Plugging in gives the n = 2 and n = 3 identities
(3)
(4)
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