Matrices play the central role in computer-aided engineering design. This chapter focuses on the methods for constructing matrices and in illustrating their applications in diverse fields. It summarizes special matrices and their main properties. MATLAB has some commonly used specialized matrices in its library that can be called when needed. Other specialized matrices, including the whole family of sparse matrices, are also included in the MATLAB library. Adding two matrices is only possible if they have equal numbers of rows and equal numbers of columns; or in other words, they both have the same size. The only modification from an all-resistors circuit is that matrices have complex numbers as elements, and the impedances have frequency dependence. The chapter explains the use of matrices as a convenient constructional tool to state and manipulate problems with some indices. It discusses analytical technique for matrix manipulation, one that is based on a generalized underlying abstract algebraic structure: the Pauli spin matrices.