with non-zero determinant, i.e. an invertible matrix. Thus, given V and y, one can find the required by solving for its coefficients in the equation :

.

That is, the map from coefficients to values of polynomials is a bijective linear mapping with matrix V, and the interpolation problem has a unique solution. This result is called the unisolvence theorem, and is a special case of the Chinese remainder theorem for polynomials.

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