No. Any scaling of the matrix will be canceled out by the matrix inverse being scaled inversely. This is because (𝛾A)−1 = 𝛾−1A−1. So,
cond(𝛾A)
= ‖𝛾A‖ · ‖(𝛾A)−1‖
= 𝛾‖A‖ · (𝛾)−1 · ‖A−1‖
= (𝛾·𝛾−1) · (‖A‖·‖A−1‖)
= 1 · (‖A‖·‖A−1‖)
= cond(A) Remember, the condition number measures the ratio of maximum stretch to minimum stretch. If both the maximum and minimum were to increase by 𝛾, the ratio wouldn't change, and therefore we have cond(𝛾A) = cond(A). Read more