Let left double bracketing bar A right double bracketing bar be the matrix norm associated with the matrix A and left bracketing bar x right bracketing bar be the vector norm associated with a vector x. Let the product A x be defined, then left double bracketing bar A right double bracketing bar and left bracketing bar x right bracketing bar are said to be compatible if left double bracketing bar A x right double bracketing bar <= left double bracketing bar A right double bracketing bar left bracketing bar x right bracketing bar .