A=
3 2 1 1
0 2 4 − 6
0 0 3 1
0 0 0 2
Figure 10-2. A 4 × 4 upper triangular matrix.
Diagonal matrices
A matrix which has zeros for all elements above and below the main diagonal is
called a diagonal matrix. Such a matrix can be described by
D= (dij), where dij = 0 for i=j.
Diagonal matrices are sometimes written D=diag (λ 1 , λ 2 ,... , λ n).The identity matrix
is an example of a diagonal matrix. Another example of a diagonal matrix is given
in the figure 10-3.
D=
3 0 0 0
0 2 0 0
0 0 5 0
0 0 0 1
Figure 10-3. Example of a 4 × 4 diagonal matrix.
Tridiagonal matrices
A matrix Asatisfying
A= (aij), where aij =
{ 0 , i > j + 10 , i < j − 1is called a tridiagonal matrix. Such a matrix is recognized as having elements along
the main diagonal and the immediate diagonals above and below the main diagonal.
All other elements within the matrix are zero. An example tridiagonal matrix is
given in the figure 10-4.
A=
3 1 0 0 0
1 2 1 0 0
0 3 3 4 0
0 0 0 2 1