Triangular Matrix
There are two types of triangular matrices: upper triangular matrix and lower triangular matrix. Triangular matrices have the same number of rows as they have columns; that is, they have n rows and n columns.
A matrix U is an upper triangular matrix if its nonzero elements are found only in the upper triangle of the matrix, including the main diagonal; that is:
uij = 0 if i > j
A matrix L is an lower triangular matrix if its nonzero elements are found only in the lower triangle of the matrix, including the main diagonal; that is:
lij = 0 if i < j
The following matrices, U and L, illustrate upper and lower triangular matrices of order n, respectively:
A unit triangular matrix is a triangular matrix in which all the
diagonal elements have a value of one; that is:
- For an upper triangular matrix, uij = 1 if i = j.
- For an lower triangular matrix, lij = 1 if i = j.
The following matrices, U and L, illustrate upper and lower unit real triangular matrices of order n, respectively:
