inverse young inequality in quaternion matrices

Inverse young inequality asserts that if v>1, then |zw|ge nu|z|^{frac{1}{nu}}+(1nu)|w|^{frac{1}{1nu}} , for all complex numbers z and w , and equality holds if and only if |z|^ 1/v= |w|^ 1/v. in this paper the complex representation of quaternion matrices is applied to establish the inverse young inequality for matrices of quaternions. moreover, a necessary and sufficient condition for equality is given.