The strict half-vectorization of an input matrix consists of the elements in the lower triangle of the matrix, excluding the elements along the diagonal of the matrix, as a column vector. The column vector is created by traversing the matrix in column-major order. The inverse strict half-vectorization takes a vector and reconstructs a symmetric matrix such that vechs2full(vechs(x)) is equal to x with zero along the diagonal if x is symmetric.
Note that very few vectors have the correct number of elements to construct a symmetric matrix. For example, vectors with 1, 3, 6, 10, and 15 elements can be used to make a symmetric matrix, but none of the other numbers between 1 and 15 can. An error is thrown if the number of elements in x cannot be used to make a symmetric matrix.