Bandwidth: The number of non-zero elements from either side of the diagonal represents half bandwidth and taken in combination, it gives the bandwidth.

Example: $$ \begin{bmatrix} 1 & -1 & 0 & 0 & 0 \\ -1 & 2 & -1 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & -1 & 2 & -1 \\ 0 & 0 & 0 & -1 & 1 \end{bmatrix} $$

The distance between '1' and '-1' in the first row is called half-bandwidth

Skyline matrix: It is also called as variable band matrix or envelop storage matrix. It is a form of sparse matrix storage format that reduces storage requirement of a matrix more than banded storage matrix.

(i) Displacement boundary condition for different supports:

a) Free support: Displacement not constrained in any direction.

b) Fixed support: u = 0, v = 0 i.e. displacement in both direction are constrained.

c) Roller support: v = 0 i.e. Displacement along the perpendicular to the line of support is constrained.

d) Pinned: u = v = 0, i.e. Displacement in both the directions is constrained.