Consider a symmetric tensor (matrix)  = Â^T which transforms a given (column) vector a into a new (column) vector b via the matrix multiplication b = ·a. Here, the superscript T denotes matrix transposition. In component form this reads b_j = ∑_k A_jk a_k, where the summation runs over all values of k from 1 to the number of spatial dimensions. Consider the scalar function f = a^T·Â·a. The equation f = const. defines a line in 2D, or a surface in 3D. For better visualization, we restrict us here to two dimensions and to the special case that both eigenvalues λ₁ and λ₂ of  are real, distinct and positive, so that the normalized eigenvectors v1,2 are orthogonal to each other. Then, any vector a can be written as av1 v1+av2 v2, and f reads f = l1 av12+l2 av22, i.e. f = const. describes an ellipse with half axes  1/l1 and 1/l2 oriented along v1 and v2.