線性代數(shù)論文

經(jīng)典word整理文檔，僅參考，雙擊此處可刪除頁眉頁腳。本資料屬于網(wǎng)絡(luò)整理，如有侵權(quán)，請聯(lián)系刪除，謝謝！[]線性代數(shù)論文題目：行列式的性質(zhì)學(xué)院：計算機科學(xué)與技術(shù)學(xué)院班級：2013級網(wǎng)絡(luò)工程本四姓名：指導(dǎo)教師：職稱：完成日期：2014年10月30日摘要：通過學(xué)習(xí)n階行列式的定義，我們知道了n階行列式共有n！項，所以直接用定義來計算n階行列式的計算量相當大，即使是用目前最快的計算機也很難實現(xiàn)。如果用定義計算一個25階行列式，需做超過251.5*1025次的乘法運算，若一個超級計算機每秒鐘能夠完成1萬億次乘法運算。用這種方法計算一個25階行列式，也將需要運算50萬年。因此如何快速的計算行列式是我們急需解決的問題，為此，我們先來研究行列式的性質(zhì)。關(guān)鍵詞：行列式；行列式的性質(zhì)；計算Abstract：Throughthedefinitionoflearningnorderdeterminant,weknowtherearennorderdeterminant!Acalculationdirectly,sotocalculatethenorderdeterminantdefinitionisquitelarge,evenifitisalsoverydifficulttoachievebyfarthefastestcomputer.Ifthecalculationofa25orderdeterminantbydefinition,needtodomorethan25!Aboutmultiplicationof1.5*1025times,ifasupercomputertocomplete1trilliontimespersecondmultiplication.Thecalculationofa25orderdeterminantinthisway,willalsoneedtobeoperationalin500000years.Therefore,tocomputethedeterminantofhowfastweneedtosolvetheproblems,therefore,wefirststudythepropertiesofdeterminant.Keywords：determinant;determinantproperty;calculation第1頁目錄1.1引言.................................................................................................................................11.1.1性質(zhì)1.....................................................................................................................................2例題.............................................................................................................................................31.1.2性質(zhì)2.....................................................................................................................................2例題.............................................................................................................................................31.1.3性質(zhì)3.....................................................................................................................................2例題.............................................................................................................................................31.1.4性質(zhì)4.....................................................................................................................................2例題.............................................................................................................................................31.1.5性質(zhì)5.....................................................................................................................................2例題.............................................................................................................................................31.1.6性質(zhì)6.....................................................................................................................................2例題.............................................................................................................................................31.1.7性質(zhì)7.....................................................................................................................................2例題.............................................................................................................................................3第2頁1.1引言設(shè)：aaaaaaaaann1aaaD,D,2nTn2aaaaaan1n2n2n則行列式DT稱為行列式D的轉(zhuǎn)置行列式。1.1.1性質(zhì)1行列式與它的轉(zhuǎn)置行列式相等。例題：1234132421.1.2性質(zhì)2例題：34212推論：若行列式的兩行（列）完全相同，則行列式為0。aaaaaa11121313331112131333DaaaDaaa11121112aaaaaa31323132D=-D,2D=0，D=01.1.3性質(zhì)3行列式的某一行（列）中所有的元素都乘同一數(shù)k，等于用數(shù)k乘此行列式。例題：123124311231DD,,2,設(shè)D=這里，DD121是用=2（1*1-2*3）2D21，即D=D12第3頁推論：行列式中某一行（列）所有元素的公因子可以提到行列式記號的外面。1.1.4性質(zhì)4行列式中如果有兩行（列）對應(yīng)元素成比例，則此行列式等于0。例題：12,這里D的第二行與第一行對應(yīng)元素之比為3，即兩行成設(shè)D36比例，由定義得1.1.5性質(zhì)5D=1*6-2*3=0例題：第i列的元素都是兩數(shù)之和：aaaa()aa,i11aa12i1naa,()D2122ii2n,aaaa()a,n1n2則D等于下列兩個行列式之和：aaaaaaaaa,ia11aa12i1n11aa121naa,iD21222,2122i2nnaaaaaaaa,n1n2n1n21.1.6性質(zhì)6把行列式的某一列（行）的各元素乘同一數(shù)，然后加到另一列（行）對應(yīng)的元素上去，行列式不變。例題：以數(shù)k乘以第j行加到第i行上，記做r+kr，有ijn2naaaaaaa1121ijai2jaan11121njkaaaaaa)ij1nc+kckakaaa)ijij()i2j2naa)n1ninjnn第4頁1.1.7性質(zhì)7式乘積之和。a推論：一個n