東南大學(xué)《線性代數(shù)》《幾何與代數(shù)》復(fù)習(xí)要點(diǎn) PPT.ppt

《東南大學(xué)《線性代數(shù)》《幾何與代數(shù)》復(fù)習(xí)要點(diǎn) PPT.ppt》由會(huì)員分享，可在線閱讀，更多相關(guān)《東南大學(xué)《線性代數(shù)》《幾何與代數(shù)》復(fù)習(xí)要點(diǎn) PPT.ppt（137頁珍藏版）》請(qǐng)?jiān)谘b配圖網(wǎng)上搜索。

1、張小向東南大學(xué)數(shù)學(xué)系東南大學(xué)數(shù)學(xué)系http:/E-mail: 1221()12( 1)nnjjjjjnjNa aa2211()12( 1)nniiNiii nia aa 運(yùn)算前提條件定義性質(zhì)加法A + BA與B是同類型的對(duì)應(yīng)元素相加A + B = B + A; (A + B) + C = A + (B + C);A + O = A; A + (A) = O數(shù)乘kAk是一個(gè)數(shù)用k乘A的每一個(gè)元素k(lA) = (kl)A; (k + l)A = kA + lA;k(A + B) = kA + kB; (1)A = A乘法ABA的列數(shù) = B的行數(shù)(aij)ml(bij)ln = (cij)mn

2、cij = (AB)C = A(BC); A(B+C) =AB+AC;(A+B)C =AC+BC; (kA)B = k(AB)冪 AmA是方陣, m是正整數(shù)A1 = A, Ak+1 = AkAAkAl = Ak+l; (Ak)l = Akl轉(zhuǎn)置AT無(aij)ml T = (aji)lm(AT)T = A; (A + B)T = AT + BT;(kA)T = kAT; (AB)T = BTAT多項(xiàng)式f(A)A是一個(gè)方陣,f(x) = asxs + a1x + a0f(A) = asAs +a1A+a0IA = ( )f(A) = f( ) ,A = ( ), f(A) = O f( ) =

3、0行列式|A|A是一個(gè)方陣, |A1| = |A|1逆矩陣A1A是一個(gè)方陣且|A|0若AB = BA = I則B = A1唯一性, (A1)1 = A, (A1)m = (Am)1,(AT)1 = (A1)T, (kA)1 = k1A1, (AB)1 = B1A1, 滿秩, 特征值01nikkjka b: : : : : (2) |B| = 2 0, B 1 =|B|1B*B11 = ( 1)1+12 14 3= 2, B21 =6, B31 = 4, B12 = 3, B22 = 6, B32 = 5, B13 = 2, B23 = 2, B33 = 2. =21 2 6 4 3 6 5 2

4、 2 2. 1 2 0 1 0 3 40 1 1A 3 1 40 2 0 1 1 2A 3 1 01 3 00 0 4A,2/ 1 0 2/ 12/ 1 0 2/ 1 0 1 0 Q.4 0 00 4 00 0 2T1 AQQAQQ;1 1 232111311 1 1|,2222332 .6/ 1 3/ 1 2/ 16/ 1 3/ 1 2/ 1 6/2 3/ 1 0 ),(321 qqqQ 3/23/13/23/23/23/13/13/23/2 3/23/13/23/23/23/13/13/23/2 1000010001 542452222 msssmmaaaaaaaaaA2122212121

5、11, : mnmmnnccccccccc 212222111211 msmmssaaaaaaaaa 212222111211 snssnnbbbbbbbbb 212222111211 mnnnmmcccccccccC212221212111, : 212222111211snssnnbbbbbbbbb 212222111211mnmmnnccccccccc mnmmnnccccccccc 212222111211 msmmssaaaaaaaaa 212222111211 snssnnbbbbbbbbb 212222111211 mnmmnnccccccccc 212222111211 msm

6、mssaaaaaaaaa 212222111211 snssnnbbbbbbbbb 212222111211 mnmmnnaaaaaaaaaA 212222111211 mnmmnnbbbbbbbbbB 212222111211 mnmmnnaaaaaaaaaA 212222111211 mnmmnnbbbbbbbbbB 2122221112110 10 1A0 00 1B0 01 1C0 00 1B1/94/9-2/9-2/91/94/94/9-2/91/9 0 37702 3520 432143214321xxxxxxxxxxxx 1 3 7 7 2 3 5 21 1 1 1 0 0 0

7、07/4 7/5 1 07/3 7/2 0 1,1 0 7/47/3 ,01 7/57/22 1 ).,( ,1 0 7/47/301 7/57/2112 14321Rccccxxxx ,11 ,1143 xx).,( ,1 1 7/ 1 7/ 11 1 7/97/511214321Rccccxxxx ,7/ 1 7/ 1 ,7/97/521 xx,1 1 7/ 1 7/ 1 ,1 1 7/97/521 1 3 7 7 2 3 5 21 1 1 1 0 0 0 0 0 1 3 4 1 0 2 5,23 1 0 ,5 40 1 21 ).,( ,23 1 0 5 40 1 21214321Rcc

8、ccxxxx 21421325 34 xxxxxx2/ 1 3 2 1 1 1 3 1 1 10 1 1 1 1 0 0 0 0 02/ 1 2 1 0 02/ 1 1 0 1 1444322421 2/ 12 2/ 1xxxxxxxxx 2/ 1 3213 0 432143214321xxxxxxxxxxxx).R,( ,0 2/ 10 2/ 11201001121214321ccccxxxx444322421 2/ 12 2/ 1xxxxxxxxx 22222211100pprrnfyyyyyy 且規(guī)范形是唯一的且規(guī)范形是唯一的. France ,233112233112aaaaa abbbbb b 特殊位置的平面特殊位置的平面 0|P Pdss111222|AxByCzDdABC121212|()|PPd ssss