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...Properties of matrices transpose and trace inner outer product computational foundations cognitive science lecture algebraic frank keller school informatics university edinburgh inf ed ac uk february addition scalar multiplication matrix zero identity mid problem denition reading anton busby ch obey the laws familiar from arithmetic with real numbers theorem if a b are scalars sizes c such that operations can be performed then cummutativelaw for associative law ab ba aa however is not cummutative i e in general there three possible reasons this dened but g both dier size same they dierent example assume...