●第 1 章 行列式·······························································································11.1 行列式的概念····················································································11.1.1 二階行列式 ·············································································11.1.2 三階行列式 ·············································································31.1.3 n 階行列式 ··············································································3習題 1.1···························································································51.2 行列式的性質····················································································6習題 1.2···························································································81.3 克萊姆法則及應用··············································································91.3.1 克萊姆法則 ·············································································91.3.2 運用克萊姆法則討論齊次線性方程組的解 ···································.10習題 1.3························································································.11復習題 1 ······························································································.12本章知識精要 ·······················································································.12第 2 章 矩陣·······························································································.142.1 矩陣的概念····················································································.14習題 2.1························································································.162.2 矩陣的性質及運算···········································································.172.2.1 矩陣相等 ·············································································.172.2.2 矩陣的運算 ··········································································.182.2.3 矩陣的轉置 ··········································································.222.2.4 方陣的行列式 ·······································································.24習題 2.2························································································.242.3 矩陣的初等變換與矩陣的秩·······························································.25線性代數VI2.3.1 矩陣的初等變換 ····································································.252.3.2 矩陣的秩 ·············································································.27習題 2.3························································································.292.4 逆矩陣··························································································.302.4.1 逆矩陣的概念 ·······································································.302.4.2 逆矩陣的性質 ·······································································.302.4.3 逆矩陣的求法 ·······································································.312.4.4 用逆矩陣解線性方程組 ···························································.34習題 2.4························································································.342.5 矩陣的應用····················································································.352.5.1 編制通信密碼 ·······································································.352.5.2 投入產出分析 ·······································································.37復習題 2 ······························································································.40本章知識精要 ·······················································································.42第 3 章 線性方程組······················································································.443.1 向量組的線性相關性········································································.443.1.1 n 維向量空間········································································.443.1.2 線性相關性概念 ····································································.453.1.3 線性相關性的判定 ·································································.45習題 3.1························································································.473.2 向量組的秩與矩陣···········································································.483.2.1 極大線性無關向量組 ······························································.483.2.2 向量組的秩 ··········································································.483.2.3 矩陣與向量組秩的關繫 ···························································.49習題 3.2························································································.493.3 線性方程組的解··············································································.503.3.法解線性方程組 ······························································.503.3.2 線性方程組解的結構 ······························································.53習題 3.3························································································.543.4 應用·····························································································.55復習題 3 ······························································································.60本章知識精要 ·······················································································.61第 4 章 相似矩陣·························································································.644.1 向量組的正交規範化········································································.64目 錄VII4.1.1 向量內積及其性質 ·································································.644.1.2 正交向量組及其性質 ······························································.654.1.3 規範正交基及其求法 ······························································.664.1.4 正交矩陣與正交變換 ······························································.67習題 4.1························································································.694.2 方陣的特征值與特征向量··································································.694.2.1 特征值與特征向量的概念 ························································.694.2.2 特征值與特征向量的基本性質 ··················································.72習題 4.2························································································.724.3 相似矩陣的概念、性質及應用····························································.724.3.1 相似矩陣的概念 ····································································.734.3.2 相似矩陣的性質 ····································································.734.3.3 矩陣與對角矩陣相似的條件 ·····················································.75習題 4.3························································································.774.4 實對稱矩陣的性質與對角化·······························································.774.4.1 實對稱矩陣的性質 ·································································.774.4.2 實對稱矩陣的對角化 ······························································.78習題 4.4························································································.82復習題 4 ······························································································.82本章知識精要 ·······················································································.83附錄 A 數學實驗指導···················································································.84附錄 B 行列式數學實驗常用指令····································································.99附錄 C 簡單的線性規劃問題··········································································101附錄 D 習題參考答案···················································································106參考文獻·····································································································114線性代數

本書在總結多年實踐教學經驗的基礎上編寫而成，主要內容包括行列式、矩陣、線性方程組、相似矩陣。全書內容簡潔、實用，同時注重數學知識與具體專業的結合，精選專業案例，將專業案例轉化為數學問題並提供解答思路。本書每章後都附帶復習題，本書的最後附有參考答案。在本書附錄中，設置數學實驗指導、行列式數學實驗常用指令、簡單的線性規劃問題等拓展內容，另外還配套部分知識點的數字化學習資源，供學習者選學或參考。在實際教學和學習中，教師和學生可根據具體的課時安排，對書中的內容進行一定程度的增補或刪減。