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Levi-Civita symbol

{c}

= Lagrange's identity
{c}
{synonym}

For three-dimensional vectors,
$$
|x\times y|^2=|x|^2|y|^2-(x\cdot y)^2.
$$
The corresponding identity in $\mathbb R^n$ is
$$
|x|^2|y|^2-(x\cdot y)^2
=\frac12\sum_{i,j}(x_iy_j-x_jy_i)^2.
$$


Lagrange identity for the cross product

Past exam of the mathematics course of the University of Cambridge / 2013 / ia / Paper 3 / 3C / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 1 / 5A / a / ii / Solution

codex/lagrange-s-identity

Lagrange identity for the cross product

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Lagrange identity for the cross product

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