Degenerate metric tensor

A symmetric bilinear form on a tangent space is degenerate when some nonzero vector pairs to zero with every vector; equivalently its matrix has zero determinant. At such a point there is no inverse metric tensor, and the usual metric tensor construction of a unique Levi-Civita connection does not apply. A coordinate expression that degenerates must be checked to distinguish a removable coordinate failure from a genuinely excluded point of the geometric domain.