Linear Systems

Often it is helpful to visualize an m x n matrix A or an m column a in block form, i.e., as a rectangle of height m and width n or 1, respectively:

The matrix A is a square matrix if m = n, and it is symmetric if addi­ tionally di^ k — &k,i-A square matrix [uiyk] is called upper triangular if Ui£ = 0 for i > k. Similarly a square matrix [/*,*] is called lower triangular if l^k — 0 for i < k. The Kronecker symbol

is used to define the identity matrix as the n x n square matrix I = [£»,*:].