A.5.12 Upper Triangular Matrices
Definition A.5.19 A matrix M, is upper triangular if Mij = 0 whenever i > j. Thus such a matrix
equals zero below the main diagonal, the entries of the form Mii as shown.
A lower triangular matrix is defined similarly as a matrix for which all entries above the main diagonal are
equal to zero.
With this definition, here is a simple corollary of Theorem A.5.16.
Corollary A.5.20 Let M be an upper (lower) triangular matrix. Then det
is obtained by
taking the product of the entries on the main diagonal.