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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.
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.