What is Sparse Matrix?
A sparse matrix is one 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.
A matrix with a wide range of zero elements is different from 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 considered a “waste” of computer memory. Lossless compression or truncated storage of a sparse matrix is a common consideration in computer science.
Typically, engineers can take into account the sparsity of the matrix and use compression methods to store only the actual values in the matrix, rather than storing a large number of elements with values of zero.
The basic nature of this compression is based on many of the same computer science concepts that allow any kind of ultra-efficient storage - techniques may include the use of pointers and references to compressed data, for example.
Some theorists describe a sparse matrix as a "loosely integrated" system where denser data imply more direct connections between data.