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Chebotar, Mikhail A.; Fong, Yuen; Lee, Pjek-Hwee
Linear algebra and its applications, 10/2005, Volume: 408Journal Article
Let A = M n ( F) be the matrix algebra over a field F with an involution ∗, where n ⩾ 20. Suppose that θ : A → A is a bijective linear map such that θ( x) θ( y) = θ( y) θ( x)* for all x, y ∈ A such that xy = yx*. We show that θ is of the form θ( x) = λuxu −1 for x ∈ A, where λ is a nonzero symmetric scalar and u is a normal matrix such that uu* is a nonzero scalar.
