41. :Matrix multiplication is performed by using a for loop inside of a for loop, not two foreach loops. 42. The basic idea comes from the associativity of matrix multiplications , and the errors are used to provide the security. 43. ;Loop nest optimization : Some pervasive algorithms such as matrix multiplication have very poor cache behavior and excessive memory accesses. 44. Using that, it follows that addition and composition of matrices obey the usual rules for matrix addition and matrix multiplication . 45. Moreover, since composition of rotations corresponds to matrix multiplication , the rotation group is isomorphic to the special orthogonal group. 46. These algorithms based on fast matrix multiplication have also been extended to problems of finding-cliques for larger values of. 47. The set of all appropriate matrices together with the operation of matrix multiplication is the rotation group SO ( 3 ). 48. For example, if a subroutine need to perform a matrix multiplication , then the subroutine would have three nested loops. 49. The Strassen's algorithm, devised by Volker Strassen in 1969 and often referred to as " fast matrix multiplication ". 50. There exist matrix multiplication algorithms with a complexity of operations, while the best proven lower bound is log ) } }.
