ABSTRACT
Problems in finite-dimensional linear algebra often reduce to the analysis of matrices. This is because of the fundamental fact that every linear operator from one finite-dimensional space to another can be represented by a matrix. The simplest kind of matrix is a diagonal matrix-a matrix whose only nonzero entries lie on the diagonal. To be precise, A ∈ Fm×n is diagonal if Aij = 0 for all i = j. In this chapter, we will restrict ourselves to the square matrices. We pursue the case of nonsquare matrices, and the special case of nonsquare diagonal matrices, in Chapter 8.
