  In the present article, a basis of the coordinate algebra of the
multi-parameter quantized matrix is constructed by using an elementary method
due to Lusztig. The construction depends heavily on an anti-automorphism, the
bar action. The exponential nature of the bar action is derived which provides
an inductive way to compute the basis elements. By embedding the basis into the
dual basis of Lusztig's canonical basis of $U_q(n^-)$, the positivity
properties of the basis as well as the positivity properties of the canonical
basis of the modified quantum enveloping algebra of type $A$, which has been
conjectured by Lusztig, are proved.
