%0 Journal Article %T Inverse Young inequality in quaternion matrices %J Wavelet and Linear Algebra %I Vali-e-Asr university of Rafsanjan %Z 2383-1936 %A Manjegani, Seyd Mahmoud %A Norouzi, Asghar %D 2016 %\ 06/01/2016 %V 3 %N 1 %P 45-52 %! Inverse Young inequality in quaternion matrices %K ‎Inverse Young inequality‎ %K Quaternion matrix %K Right eigenvalue‎ %K ‎Complex representation %R %X Inverse 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. %U https://wala.vru.ac.ir/article_19953_35469da2a28c83b1b25944b53b87c748.pdf