= Haar measure from a left-invariant coframe
{c}
{title2=$d\mu=|\theta^1\wedge\cdots\wedge\theta^d|$}
On a $d$-dimensional <Lie group>, take the <coframe> dual to a basis of <left-invariant vector fields>. Its top wedge is nonvanishing and invariant under left translations, so its absolute density defines a left <Haar measure>. If the frame has coordinate matrix $A(x)$, the density is $|\det A(x)|^{-1}dx^1\cdots dx^d$. This makes explicit computation of Haar measure a determinant calculation.
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