Can represent a symmetric bilinear form as shown at matrix representation of a symmetric bilinear form, or a quadratic form.

The definition implies that this is also a symmetric matrix.

The dot product is a positive definite matrix, and so we see that those will have an important link to familiar geometry.

WTF is a skew? "Antisymmetric" is just such a better name! And it also appears in other definitions such as antisymmetric multilinear map.