**Answer:**

**Sparse Matrix**

A matrix is a two-dimensional object with a total of m x n values made up of m rows and n columns. If most of the matrix elements are worth 0, then Its is called sparse matrix.

or,

Matrices with a relatively high proportion of zero entries are called sparse matrices. Two general types of n-square sparse matrices, which occur in various applications, are:

**Tridiagonal Matrix****Triangular Matrix**

The triangular matrix, where all entries where above the main diagonal are zero equivalently where zero entries can only occur on or below the main diagonal is called a lower **Triangular Matrix**.

The matrix, where non-zero entries can only occur on the diagonal or on elements immediately above or below the diagonal is called a **Tridiagonal matrix**.

The natural method of representing matrices in memory as 2-D arrays may not be suitable for sparse matrices. That is, one may save space by storing

only those entries, which may be non-zero. This can be explained with the following example:

**Non-zero element are:**

M[1][3] = 6, M[1][5] = 9,

M[2][1] = 2, M[2][4] = 7,

M[2][5] = 8, M[2][7] = 4,

M[3][1] = 10, M[4][3] = 12,

M[6][4] = 3,M[6][4] = 5;

One of the basic methods for storing such, a sparse matrix is to store non-zero elements in a one-dimensional array and to identify each array element with row and column indices as:

The **ith** element of vector V is the matrix element with row; column indices **Row[i]** and **Col[i]**.