Sometimes the notation formula_80 is used instead of formula_5 for the skew-symmetric matrix. This is a particularly unfortunate choice as it leads to confusion with the notion of a complex structure, which often has the same coordinate expression as formula_5 but represents a very different structure. A complex structure formula_80 is the coordinate representation of a linear transformation that squares to formula_84, whereas formula_5 is the coordinate representation of a nondegenerate skew-symmetric bilinear form. One could easily choose bases in which formula_80 is not skew-symmetric or formula_5 does not square to formula_84.