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A sparse matrix is a matrix in which many or most of the elements have a value of zero. This is in contrast to a dense matrix, where many or most of the elements have a non-zero value. Sparse matrices are used in specific ways in computer science, and have different data analysis and storage protocols and techniques related to their use.
Techopedia Explains Sparse Matrix
Having a matrix with a wide range of zero elements is different than having a matrix with a range of full values. One of the biggest differences is that storing the entire sparse matrix in a digital format is seen as “wasting” computer memory. The lossless compression or truncated storage of a sparse matrix is a common consideration in computer science.
Typically, engineers can consider the sparsity of the matrix and use compression methods to only store the actual values in the matrix, rather than storing a large number of elements with values of zero. The fundamental nature of this compression is based on many of the same computer science concepts that allow any kind of ultra-efficient storage – techniques, for example, can include the use of pointers and references to compressed data.
Some theoreticians describe a sparse matrix as representing a more “loosely integrated” system,where denser data implies more direct connections between data.
