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Sec. 12.2 Matrix Representations 411Cols0 1 3 6Rows00,0 0,1 0,610 231910,3 1,1 1,345 5 9340,44077,1 7,3 7,632 12 7Figure 12.7 The orthogonal list sparse matrix representation.the sparse matrix requires. The size of the sparse matrix depends on the numberof non-zero elements (we will refer to this value as NNZ), while the size of thestandard matrix representation does not vary. We need to know the (relative) sizesof a pointer and a data value. For simplicity, our calculation will ignore the spacetaken up by the row and column header (which is not much affected by the numberof elements in the sparse array).As an example, assume that a data value, a row or column index, and a pointereach require four bytes. An n × m matrix requires 4nm bytes. The sparse matrixrequires 28 bytes per non-zero element (four pointers, two array indices, and onedata value). If we set X to be the percentage of non-zero elements, we can solvefor the value of X below which the sparse matrix representation is more spaceefficient. Using the equation28X = 4mnand solving for X, we find that the sparse matrix using this implementation is morespace efficient when X < 1/7, that is, when less than about 14% of the elements