In mathematics, Cartan's lemma refers to a number of results named after either Élie Cartan or his son Henri Cartan:
- In exterior algebra:[1] Suppose that v1, ..., vp are linearly independent elements of a vector space V and w1, ..., wp are such that
- in ΛV. Then there are scalars hij = hji such that
- so that . Let K2, ..., Kn be simply connected domains in C and let
- so that again . Suppose that F(z) is a complex analytic matrix-valued function on a rectangle K in Cn such that F(z) is an invertible matrix for each z in K. Then there exist analytic functions in and in such that
- in K.