chap patterns of algorithms matrix multiplication the standard algorithm for multiplying two matrices requires th( time it is possible to do better than this by rearranging and grouping the multiplications in various ways one example of this is known as strassen' matrix multiplication algorithm for simplicitywe will assume that is power of two in the followinga and are arrayswhile aij and bij refer to arrays of size / / using this notationwe can think of matrix multiplication using divide and conquer in the following way of courseeach of the multiplications and additions on the right side of this equation are recursive calls on arrays of half sizeand additions of arrays of half sizerespectively the recurrence relation for this algorithm is ( ( / ( / ) th( this closed form solution can easily be obtained by applying the master theorem strassen' algorithm carefully rearranges the way that the various terms are multiplied and added together it does so in particular orderas expressed by the following equation in other wordsthe result of the multiplication for an array is obtained by different series of matrix multiplications and additions for / / arrays multiplications between subarrays also use strassen' algorithmand the addition of two subarrays requires th( time the subfactors are defined as followss ( ( ( ( ( ( ( ( ( (