ex3.设4=(an)是m阶正定矩阵证明ai>0i=1,2,…,n) Proof.∵x!Ax>0, 取x=(0,…,0,1,0,…,0)y, n 则 CAr= (0 n nn >0 结论成立 Kex3. A (a ) n , a 0(i 1,2, ,n). 设 = i j 是 阶正定矩阵 证明 i i  =  Proof.  xAx  0, 取 x = (0,  ,0,1,0,  ,0) , ( )                                  = 0 1 0 0 1 0 1 1 1 1 1 1                     n ni nn i i i i n i n a a a a a a a a a 则 x Ax =  0. aii 结论成立