Uniform Symbols

Classical mathematical physics uses various scalar, vector and tensor notations, depending on the discipline, but for simplicity and uniformity I will use matrices operators (differential or physical), and vectors for the object or outcome of operators. Thus, for example, a second rank tensor with index range three is represented as a 3x3 matrix. Similarly, an even higher order tensor such as the elastic stiffness can be written in matrix form. The matrix representation is a widely accepted tool for complex mathematical descriptions and seems to give a more pictorial description of the physical processes. Moreover, besides the ease of representation, numerical applications benefit from efficient matrix algebra.