Chapter 9 The Transitive Closure, All Pairs Shortest Paths
... R is computed in lg(n-1) + 1 matrix multiplications. Each multiplication requires O(n3) operations so R can be computed in O(n3 * lgn) 9.6.1 Kronrod's Algorithm It is used to multiply boolean matrices. C = A x B For example suppose: The A matrix row determines which rows of B are to be unioned to pr ...
... R is computed in lg(n-1) + 1 matrix multiplications. Each multiplication requires O(n3) operations so R can be computed in O(n3 * lgn) 9.6.1 Kronrod's Algorithm It is used to multiply boolean matrices. C = A x B For example suppose: The A matrix row determines which rows of B are to be unioned to pr ...
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... satisfying γ(0) = I, and γ " (0) = B. Now it just remains to be seen that γ is a curve in GLn (R), and this will be true if # is chosen carefully based on the determinant of B such that I + tB will be in the ball around I and det(I + tB) '= 0. Thus TGLn (R) = Mn (R) and dim(GLn (R)) = n2 ...
... satisfying γ(0) = I, and γ " (0) = B. Now it just remains to be seen that γ is a curve in GLn (R), and this will be true if # is chosen carefully based on the determinant of B such that I + tB will be in the ball around I and det(I + tB) '= 0. Thus TGLn (R) = Mn (R) and dim(GLn (R)) = n2 ...
A summary of matrices and matrix math
... Probably the more commonly used mode of matrix multiplication, distinct from simple multiplication by component as described above, involves the use of dot products. Two matrices can be multiplied using dot products if the number of rows in one matrix equals the number of columns in the other matrix ...
... Probably the more commonly used mode of matrix multiplication, distinct from simple multiplication by component as described above, involves the use of dot products. Two matrices can be multiplied using dot products if the number of rows in one matrix equals the number of columns in the other matrix ...
