Inverse Young inequality in quaternion matrices

Inverse Young inequality asserts that if nu >۱, then |zw|ge nu|z|^{frac{۱}{nu}}+(۱-nu)|w|^{frac{۱}{۱-nu}}, for all complex numbers z and w, and equality holds if and only if |z|^{frac{۱}{nu}}=|w|^{frac{۱}{۱-nu}}. 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.

Keywords:

‎Inverse Young inequality‎ , Quaternion matrix , Right eigenvalue‎ , ‎Complex representation