Approved for OTS releaw

SUMMARY; When a matrix la represented as a product of "elementary" matrices, the matrix, its transpose, Its Inverse and inverse trans-pose are readily available for vector multiplication. 3y an "elementary matrix " Is meant one formed from the identity matrix by replacing one column; thus an elementary matrix can be com-pactly recorded by the subscript of the altered column and the values of the elements in it. In the revised simplex method {tjv both the inverse and inverse transpose of a "basic " matrix are needed; more significant, however, is the fact that each itera-tion replaces one of the columns of the basis. In the product form of representation, this change can be conveniently effected by multiplying the previous matrix by an elementary matrix; thus, only one additional column of information need be recorded with each iteration. This approach places relatively greater emphasis on reading operations than writing and thereby reduces com