Symmetric function
Definition
A bivariate function $f : X \times X \to Y$ is called a symmetric function if it satisfies the following condition.
Conversely, a function $f$ is called a skew-symmetric function if it satisfies the following condition.
Explanation
A symmetric matrix is a matrix that satisfies $A = A^{\mathsf{T}}$; in finite dimension this corresponds to a symmetric bilinear form.