Subspace

A sub­space \(U=(F_U, V_U)\) of a Vec­tor space \(W=(F_W, V_W)\) is a vec­tor space where \(F_U = F_W\) and \(V_U\) is a sub­group of \(V_W,\) and \(V_U\) is closed un­der scalar mul­ti­pli­ca­tion.