Abstract. We improve on Jarník's inequality between uniform Diophantine exponent $\alpha $ and ordinary Diophantine exponent $\beta $ for a system of $ n\ge2$ real linear forms in two integer variables. Jarník (1949, 1954) proved that $\beta\ge \alpha(\alpha -1)$. In the present paper we give a better bound in the case $\alpha >1$.

AMS Subject Classification (1991): 11J13

Keyword(s): Diophantine exponents, linear forms, best approximations

Received September 11, 2012, and in revised form February 6, 2012. (Registered under 68/2012.)