Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363120160601Inverse Young inequality in quaternion matrices455219953ENSeyd MahmoudManjeganiDepartment of Mathematical Sciences, Isfahan University of Technology,
Isfahan, Islamic Republic of IranAsgharNorouziDepartment of Mathematical Sciences, Isfahan University of Technology,
Isfahan, Islamic Republic of IranJournal Article20151103Inverse Young inequality asserts that if $nu >1$, then $|zw|ge nu|z|^{frac{1}{nu}}+(1-nu)|w|^{frac{1}{1-nu}}$, for all complex numbers $z$ and $w$, and equality holds if and only if $|z|^{frac{1}{nu}}=|w|^{frac{1}{1-nu}}$. 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.http://wala.vru.ac.ir/article_19953_35469da2a28c83b1b25944b53b87c748.pdf