Working in a fixed basis, "ω" can be represented by a matrix. The conditions above are equivalent to this matrix being skew-symmetric, nonsingular, and hollow. This should not be confused with a symplectic matrix, which represents a symplectic transformation of the space. If "V" is finite-dimensional, then its dimension must necessarily be even since every skew-symmetric, hollow matrix of odd size has determinant zero. Notice that the condition that the matrix be hollow is not redundant if the characteristic of the field is 2. A symplectic form behaves quite differently from a symmetric form, for example, the scalar product on Euclidean vector spaces.