Linear transformations on matrices
Marvin D. Marcus · Journal of Research of the National Bureau of Standards Section B Mathematical Sciences · 1971
Let K be a fi e ld and let M .. (K) de note th e vec tor SIJace of a ll n X n matri ces over K. S u ppose J(X) is a n invariant de fin ed on a s ubse t ~[ o f M .. (K ) .This pape r s urveys certain res ults conce rnin g the followin g probl em.Describ e th e se t .2? (I, ~l) of a ll lin ea r tra nsforma tio ns T: ~ -> ~ th at hold the invariant J fix ed: J(T(X)) = J(X), Key words: Matri ces; inva ri a nts; de te rminant; ge nera lized matrix fun c ti on; rank .