In 1980 cline and greville gave the definition of the w - weighted drazin inverse which is the extension of drazin inverse . from then on many people studied the w - weighted drazin inverse in different fields Cline和greville于1980年提出长方阵的加权drazin逆的概念,它是方阵的drazin逆的推广,有其实用背景。