AX=B →X=B/A, C=BX,…

Other than save space, with both quality and quantity, vectors are qualified as the systems monitoring tools, as they form a Group of multiplication, provided a component wise multiplication.

All of us uses worksheet and do the vector multiplication all the time, now. People may take it as granted, but that is not true. In science research, nothing is granted. There must be someone who worked out, put in publication or registered for copyright. WHO is the first one to define componentwise vector multiplication, and inverse? If there is no citation stating otherwise, then I would say, the CSU research associate, Dr. T. Jay Bai, is the first one to give definition of vector component wise multiplication, inverse, and division, (registered for copyright and published paper on 1995 and 1997, respectively.) That makes vectors a Group of Multiplication, and makes systems transition available, and that makes System Monitoring possible.