explain concept of a sparse matrix and its representation using arrays.

explain concept of a sparse matrix and its representation using arrays.

A sparse matrix is a matrix in which most of the elements are zero. In many applications, especially those involving large matrices, only a small fraction of the matrix elements are non-zero. Storing and processing large matrices with many zero elements can be inefficient if using a standard dense matrix representation.

A sparse matrix is a matrix with a majority of zero elements, and efficient representations are crucial for handling large matrices. Common representations include:

• Coordinate List (COO): Stores non-zero values with their row and column indices.
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• Compressed Sparse Row (CSR): Stores non-zero values by row, with separate arrays for values, column indices, and row pointers.
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• Compressed Sparse Column (CSC): Stores non-zero values by column, with separate arrays for values, row indices, and column pointers.
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Each representation has its advantages and is suited for different types of operations and use cases in numerical computing and data analysis.