Linear Algebra II: Advanced Topics for Applications

This is the second volume of the two-volume book on linear algebra in the University of Tokyo (UTokyo) Engineering Course.The objective of this second volume is to branch out from the standard mathematical results presented in the first volume to illustrate useful specific topics pertaining to engineering applications. While linear algebra is primarily concerned with systems of equations and eigenvalue problems for matrices and vectors with real or complex entries, this volumes covers other topics such as matrices and graphs, nonnegative matrices, systems of linear inequalities, integer matrices, polynomial matrices, generalized inverses, and group representation theory.The chapters are, for the most part, independent of each other, and can be read in any order according to the reader's interest. The main objective of this book is to present the mathematical aspects of linear algebraic methods for engineering that will potentially be effective in various application areas.

這是東京大學（UTokyo）工程課程中關於線性代數的兩卷書的第二卷。第二卷的目標是從第一卷中呈現的標準數學結果中分支出來，以展示與工程應用相關的有用特定主題。雖然線性代數主要涉及實數或複數元素的矩陣和向量的方程組和特徵值問題，但這本書涵蓋了其他主題，如矩陣和圖形、非負矩陣、線性不等式系統、整數矩陣、多項式矩陣、廣義逆和群表示理論。這些章節大部分是獨立的，讀者可以根據興趣按任意順序閱讀。這本書的主要目標是介紹線性代數方法在工程領域中的數學方面，這些方法在各種應用領域中可能非常有效。