File:NLC416-08jh009950-8831 行列式之理論及其應用.pdf

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行列式之理論及其應用   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
司各脫(R. F. Scott)著
image of artwork listed in title parameter on this page
Title
行列式之理論及其應用
Publisher
商務印書館[發行者] (上海)
Description

目錄
第一篇 行列式之理論
第一章 緒論
1，2 記法一次方程式
3 sarrus氏法則
4-6 第三級行列式之初等性質
7，8 兩行列式之積
第二章 定義及記法正負更迭數
1-7 單元之排列
8-10 行列式之一般定義
11 行及列之互換
12-14 正負更迭數
15 以正負更迭數之積表行列式之式
16，17 例
第三章 行列式之一般性質
1，2 行及列之互換
3，4 當行列式一行上單元為他數之和時行列式之值
5，6 例
7 一次方程式組之解法
第四章 小行列式及行列式之展開式
1 第p級小行列式之數
2-4 相余小行列式
5 laplace氏定理
6，7 例
9-11 行列式按一行上單元而展開之展開式
12-14 例
15，16 行列式之微係數
18-21 行列式其單元為多項式時之albeggiani氏展開式
22，23 行列式按主對角線上單元之積而展開之展開式
24 cauchy氏定理
25 例
第五章 陣之合併行列式之乘法
1-4 合併兩陣而成之行列式
5-7 例
8 由laplace氏定理導出之基本定理
9 積行列式之小行列式
10 積行列式之微係數
第六章 繁行列式
1-3 反應陣
4，5 第一級反應陣
6，7 例
8-11 第m級反應陣
12-16 sylvester氏之定理及其他
17 netto氏定理
18，19 kronecker氏定理
20，21 兩獨立組之場合
第七章 行列式之數值性質原始因式
1 一般行列式不可分解
2-4 行列式因式及原始因式之定義
5-8 合法小行列式原始因式之性質
9 等值陣
10-13 化為標準形之法
第八章 特殊形之行列式
1-3 對稱行列式
4-8 變及變對稱行列式
9-16 變對稱行列式為pfaff氏式
17，18 變行列式之例
20-22 正交對稱行列式
23-26 單元為輪換排列之行列式
27-30 單元為二項式係數之行列式
第九章 立方形行列式及多個足指數之行列式
1，2 定義，記法
3 以正負更迭數之積表立方行列式之式
4-9 立方行列式之初等性質
10-18 多個足指數之行列式
19，20 例
第十章 無窮級行列式
1-4 定義
5-9 模範行列式之性質
10 積之定理
11，12 半模範行列式
第二篇 行列式之應用
第十一章 行列式在方程式及消去法理論上之應用
1-6 一次方程式組
7-9 一次代入式
10-15 消去及判別式
16 bezout氏行列式之性質
17，18 二次式組及一次式組
19 sylvester氏對於〓全含實根之證明
第十二章 有理函數之行列式
1-3 n數兩量之差之積
4-17 函數行列式之例
第十三章 jacobi式及hesse式
1 jacobi式之定義及記法
2 非獨立函數之jacobi式等零
3-5 有公因式之函數之jacobi式
6-10 jacobi式之性質
11 bertrand氏定義
12 由正負更迭數而下之定義
13，14 高級積分式之變換式
15 hesse氏定義及例
16 jacobi式及hesse式乃共變式
17 n個一次函數之jacobi式，二次式之hesse式
第十四章 對於復一次式及二次式之應用
1-3 復一次之記號乘法
4 特性方程式
5-7 記號演算法之應用
8，9 kronecker氏定理之frobenius氏證明
10-15 復一次式及二次式之化法
16，17 兩二次式之共化法
18-24 正交代入式
25 以立方行列式表二次式之不變式
第十五章 同變數函數之行列式
1-9 定義，初等性質
10 一次微分方程式之應用
11 jacobi氏方程式之hesse氏解法
第十六章 連分數理論上之應用
1 遞升及遞降連分數
2-7 表遞降連分數之漸近值之式
8，9 遞升連分數，及由此種化為遞降連分數之法
10 化級數為連分數之法
11 fuerstenau氏對於連分數之推廣
第十七章 幾何學上之應用
1-3 三角形之面積，四面體之體積
4-6 初等全等式
7 正負更迭數之應用
8-14 直線間之夾角，立體角，球面圖形
15-18 直線組，線坐標，相對力距
19-23 連結空間內五點之直線間關係式（cayley），四面體之體積，三角形之面積siebeck氏定理
24-28 關於橢圓面之公式，球面上六點之cayley氏定理faure氏指數理論
29-39 球組，位置冪數，公切線
問題
史略
術語索引
人名索引

Language Chinese
Publication date 民國24[1935]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
主題
InfoField
行列式
中圖分類
InfoField
O151.22
拼音題名
InfoField
hang lie shi zhi li lun ji qi ying yong
載體形態
InfoField
397頁

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