東南大學《線性代數(shù)》《幾何與代數(shù)》復(fù)習要點 PPT.ppt
張小向東南大學數(shù)學系東南大學數(shù)學系http:/E-mail: 1221()12( 1)nnjjjjjnjNa aa2211()12( 1)nniiNiii nia aa 運算前提條件定義性質(zhì)加法A + BA與B是同類型的對應(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是一個數(shù)用k乘A的每一個元素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 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多項式f(A)A是一個方陣,f(x) = asxs + a1x + a0f(A) = asAs +a1A+a0IA = ( )f(A) = f( ) ,A = ( ), f(A) = O f( ) = 0行列式|A|A是一個方陣, |A1| = |A|1逆矩陣A1A是一個方陣且|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 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 msssmmaaaaaaaaaA212221212111, : mnmmnnccccccccc 212222111211 msmmssaaaaaaaaa 212222111211 snssnnbbbbbbbbb 212222111211 mnnnmmcccccccccC212221212111, : 212222111211snssnnbbbbbbbbb 212222111211mnmmnnccccccccc mnmmnnccccccccc 212222111211 msmmssaaaaaaaaa 212222111211 snssnnbbbbbbbbb 212222111211 mnmmnnccccccccc 212222111211 msmmssaaaaaaaaa 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 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 21214321Rccccxxxx 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
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