(完整版)高等代數(shù)知識(shí)點(diǎn)歸納,推薦文檔

1、ai1aj1+ ai 2aj 2+lainajn a , i = j,= 0, i j.第 4 頁(yè)共 7 頁(yè)=*ao = aobobao = a b* boa = *a = (-1)mn a bbobo*nan1a2n-1a1nooa1n=a2n-1nan1on ( n-1)( 1) a a= -2ka1n 2nn1范德蒙德行列式：11l1x1x2x2x2lxnlx2= (x - x )12nmmm12nxn-1xn-1lxn-11 jinij代數(shù)余子式和余子式的關(guān)系： m = (-1)i+ j aa = (-1)i+ j mijijijij a b a b an分塊對(duì)角陣相乘： a = 11

2、a , b = 11b ab =11 11a b , an = 11an 22 22 22 22 22 ab t分塊矩陣的轉(zhuǎn)置矩陣： cd at= btct dt 21 a11alan1 taalaa* = (a ) = 1222n2 ， a 為 a 中各個(gè)元素的代數(shù)余子式.ij mmm ijaala 1n2nnn aa* = a* a = a e , a* = a n-1 ,a-1 = a -1 . a*分塊對(duì)角陣的伴隨矩陣： b ba*= ab* 矩陣轉(zhuǎn)置的性質(zhì)：( at )t = a( ab)t = bt atat = a( a-1)t = ( at )-1( at )* = ( a*

3、)t矩陣可逆的性質(zhì)：( a-1)-1 = a( ab)-1 = b-1a-1a-1 = a -1( a-1)k = ( ak )-1 = a-k伴隨矩陣的性質(zhì)：( a* )* = a n-2 a( ab)* = b* a*a* = a n-1( a-1 )* = ( a* )-1 = aa( ak )* = ( a* )k n若r( a) = nr( a* ) = 1若r( a) = n -10若r( a) 0.正定矩陣正定二次型對(duì)應(yīng)的矩陣.4. f (x) = xt ax 為正定二次型 （之一成立）：（1） x a ， xt ax 0 ；（2） a 的特征值全大于0 ；（3） f 的正慣性指

4、數(shù)為 n ；（4） a 的所有順序主子式全大于0 ；（5） a 與 e 合同，即存在可逆矩陣c 使得ct ac = e ；（6） 存在可逆矩陣 p ，使得 a = pt p ； a可逆 r( a) = n a的列（行）向量線性無(wú)關(guān) a的特征值全不為0 ax =a只有零解 x a，a aa 0 a rn , ax = a總有唯一解 at a是正定矩陣 a e a = p p p p 是初等陣1 2si 存在階矩陣使b得, 或a b = eab = e a不可逆 r( a) n a = 0 a的列（行）向量線性相關(guān) 0是的特征值 ax =a有非零解, 其基礎(chǔ)解系即為a 于0的=特征向量“”“”at

5、 the end, xiao bian gives you a passage. minand once said, people who learn to learn are very happy people. in every wonderful life, learning is an eternal theme. as a professional clerical and teaching position, i understand the importance of continuous learning, life is diligent, nothing can be ga

6、ined, only continuous learning can achieve better self. only by constantly learning and mastering the latest relevant knowledge, can employees from all walks of life keep up with the pace of enterprise development and innovate to meet the needs of the market. this document is also edited by my studio prof