A note on unique solvability of the absolute value equation

In this note, we show that the singular value condition $$\sigma _{\max }(B) < \sigma _{\min }(A)$$ σ max ( B ) < σ min ( A ) leads to the unique solvability of the absolute value equation $$Ax + B|x| = b$$ A x + B | x | = b for any b . This result is superior to those appeared in previously published works by Rohn (Optim Lett 3:603–606, 2009).

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