Sparse Matrix

A sparse matrix is a matrix in which most of the elements are zero. In contrast, a dense matrix is a matrix in which most of the elements are non-zero. Sparse matrices are common in various applications where efficiency in terms of storage and computation is crucial.

In sparse matrices, only the non-zero elements and their indices are stored, which can significantly reduce memory usage. This storage scheme is particularly useful when dealing with large matrices that are mostly empty.

There are several methods for representing sparse matrices, including:

• Dictionary of Keys (DOK): Stores the elements as key-value pairs.
• Compressed Sparse Row (CSR): Stores the row indices, column indices, and values separately.
• Compressed Sparse Column (CSC): Similar to CSR but stores the column indices instead.
• List of Lists (LIL): Uses lists of lists to represent the matrix.

Sparse matrices find applications in various fields, such as scientific computing, machine learning, graph theory, and more. They are particularly useful in situations where the data is sparse, and storing all elements would be inefficient.

Efficient algorithms have been developed to perform operations on sparse matrices, taking advantage of