There are faster ways to multiply sparse matrices, and we will deal with these matrices in Chapters 21 and 22. A matrix most of whose entries are zero is called sparse. To multiply two 100 × 100 matrices involves computing 1,000,000 products. For example, if the matrices have dimension 10 × 10, the computation of their product requires 1000 multiplications. If A and B are both n × n matrices, n 3 multiplications must be performed. There are m rows in AB, so the total number of multiplications is m ( kn) = mkn. ![]() This must be done n times to form each row of AB, so the computation of a row of AB requires kn multiplications. The computation of ( AB) ij requires calculating k products. Consider computing the product of an m × k matrix A and a k × n matrix B. On a computer, multiplication is a much more time-consuming operation than addition. Matrix multiplication is a computationally expensive operation.
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