秩:与通常矩阵秩的定义相同 (1)Q(s)非零,1≤rmkQ(s)≤mn(q,p); (2)rmkQ(s)=r台Q(s)有且仅有r个列行线性无关 (3)Q(s满秩分→rmkQ(s)=mi(q,p) (4)Q(s),Q(s)非奇异分 ranko(s)=p;Q(s)奇异台 ranko(s)<p; (5)Q(s)前乘或后乘非奇异多项式矩阵,其秩不变,即 rank(s)=rankpaxo (s)o(s=ranksrox(s) (6rankosr(s)smin ranke(s), rank(s)• 秩：与通常矩阵秩的定义相同 (6) ( ) ( ) min[ ( ), ( )] ( ) ( ) ( ) ( ) ( ) (5) ( ) , , (4) ( ), ( ) ( ) ; ( ) ( ) ; (3) ( ) ( ) min( , ); (2) ( ) ( ) ( ) ; (1) ( ) ,1 ( ) min( , ); rankQ s R s rankQ s rankR s rankQ s rankP s Q s rankQ s R s Q s Q s Q s rankQ s p Q s rankQ s p Q s rankQ s q p rankQ s r Q s r Q s rankQ s q p q q p p q p p p  = =  =    = =        前乘或后乘非奇异多项式矩阵 其秩不变 即 非奇异 奇异 满秩 有且仅有 个列 行 线性无关 非零