A square matrix A is called a band matrix, if its entries vanish outside some band parallel to the main
diagonal.
If ms is the number of sub-diagonals of A and mr the number of super-diagonals of A, then m = ms + mr +1 is the bandwidth of A .
A matrix A of bandwidth m can have at most m non-zero elements in any one row. The following are special band matrices:
| · | Diagonal Matrix: m = 1, ms = mr = 0 |
| · | Bidiagonal Matrix: m = 2, ms = 0 and mr = 1, or ms = 1 and mr = 0 |
| · | Tridiagonal Matrix: m = 3, ms = mr = 1 |
| · | Five-Diagonal Matrix: m = 5, ms = mr = 1 |
A square matrix An is called a cyclically tridiagonal matrix, if aij = 0 for 1 < |i-j| < n-1.
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