A First Course in Linear Algebra (Paperback)

A First Course in Linear Algebra is written by two experts from algebra who have more than 20 years of experience in algebra, linear algebra and number theory. It prepares students with no background in Linear Algebra. Students, after mastering the materials in this textbook, can already understand any Linear Algebra used in more advanced books and research papers in Mathematics or in other scientific disciplines. This book provides a solid foundation for the theory dealing with finite dimensional vector spaces. It explains in details the relation between linear transformations and matrices. One may thus use different viewpoints to manipulate a matrix instead of a one-sided approach. Although most of the examples are for real and complex matrices, a vector space over a general field is briefly discussed. Several optional sections are devoted to applications to demonstrate the power of Linear Algebra.

《線性代數初階課程》是由兩位在代數領域擁有超過20年經驗的專家所撰寫。本書針對沒有線性代數背景的學生進行準備。學生在掌握本教材後，已能理解數學或其他科學領域中更高階書籍和研究論文中所使用的任何線性代數。本書為有限維向量空間理論提供了堅實的基礎。詳細解釋了線性變換和矩陣之間的關係。因此，可以使用不同的觀點來操作矩陣，而不僅僅是單一的方法。雖然大部分的例子都是針對實數和複數矩陣，但也簡要討論了一般域上的向量空間。還有幾個選擇性的章節專門用於應用，以展示線性代數的威力。