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Mathematica is "aware" of linearity of Dot in all its arguments, but to exploit it you need to tell Mathematica which expressions represent Matrices, and explicitly ask to expand expression using … TensorExpand function: ClearAll[α, β, γ, δ, a, b, c, d, k, l, m, n] TensorExpand[ Dot[α a, β b + γ c, δ d], Assumptions -> a ∈ Matrices[{k, l}] && (b|c) ∈ Matrices[{l, m}] && d …
answered Mar 8 '16 by jkuczm