Trapezoidal Matrix
There are two types of trapezoidal matrices: upper trapezoidal matrix and lower trapezoidal matrix. Trapezoidal matrices have m rows and n columns.
A matrix U is an upper trapezoidal matrix if its nonzero elements are found only in the upper triangle of the matrix, including the main diagonal; that is:
A matrix L is an lower trapezoidal matrix if its nonzero elements are found only in the lower triangle of the matrix, including the main diagonal; that is:
The following matrices, U and L, illustrate upper and lower trapezoidal matrices with m rows and n columns, respectively:
If m ≥ n:
If m < n:
- For an upper trapezoidal matrix, uij = 1 if i = j.
- For a lower trapezoidal matrix, lij = 1 if i = j.
The following matrices, U and L, illustrate upper and lower unit real trapezoidal matrices with m and n columns, respectively:
If m ≥ n:
If m < n:
