Unformatted text preview: A ) of a square matrix A is deﬁned to be the sum of the diagonal entries A ii . Show that for all A ∈ M m × n ( F ) and B ∈ M n × m ( F ), we have tr( AB ) = tr( BA ) . (Note that AB is m × m and BA is n × n , so they are square matrices.) 5. Let A be a matrix over F . Prove that rank( L A ) = 1 if and only if there exist a nonzero row vector X and a nonzero column vector Y such that A = Y X ....
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 Fall '08
 GUREVITCH
 Linear Algebra, Algebra, Transformations, Vector Space, Sets, finitedimensional vector space, nonzero column vector, nonzero row vector

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