sec matrix representations element also stores pointers to its non-zero neighbors following and preceding it in the column thuseach non-zero element stores its own valueits position within the matrixand four pointers non-zero elements are found by traversing row or column list note that the first non-zero element in given row could be in any columnlikewisethe neighboring non-zero element in any row or column list could be at any (higherrow or column in the array thuseach non-zero element must also store its row and column position explicitly to find if particular position in the matrix contains non-zero elementwe traverse the appropriate row or column list for examplewhen looking for the element at row and column we can traverse the list either for row or for column when traversing row or column listif we come to an element with the correct positionthen its value is non-zero if we encounter an element with higher positionthen the element we are looking for is not in the sparse matrix in this casethe element' value is zero for examplewhen traversing the list for row in the matrix of figure we first reach the element at row and column if this is what we are looking forthen the search can stop if we are looking for the element at row and column then the search proceeds along the row list to next reach the element at column at this point we know that no element at row and column is stored in the sparse matrix insertion and deletion can be performed by working in similar way to insert or delete elements within the appropriate row and column lists each non-zero element stored in the sparse matrix representation takes much more space than an element stored in simple matrix when is the sparse matrix more space efficient than the standard representationto calculate thiswe need to determine how much space the standard matrix requiresand how much the sparse matrix requires the size of the sparse matrix depends on the number of nonzero elementswhile the size of the standard matrix representation does not vary we need to know the (relativesizes of pointer and data value for simplicityour calculation will ignore the space taken up by the row and column header (which is not much affected by the number of elements in the sparse arrayas an exampleassume that data valuea row or column indexand pointer each require four bytes an matrix requires nm bytes the sparse matrix requires bytes per non-zero element (four pointerstwo array indicesand one data valueif we set to be the percentage of non-zero elementswe can solve for the value of below which the sparse matrix representation is more space efficient using the equation mnx mn