Li Jiong-sheng's Linear Algebra, written by Chinese University of Science and Technology, should be regarded as the most detailed, and it can be said to be an excellent textbook in terms of both writing techniques and content.

In addition, A Concise Course of Advanced Algebra in Peking University is also an excellent book, which downplays matrix skills, highlights transformation ideas and highlights algebraic thinking mode.

In addition, Introduction to Algebra by Costell King of the Soviet Union is also a good book.

In a word, I personally think that a good algebra book must emphasize the concepts of space and transformation, because this is an important basis for continuing to learn other branches of algebra in the future. As for matrix skills, unless you decide to study matrix theory in the future, you can dilute them appropriately.

Therefore, from this perspective, Xu Yichao's Linear Algebra and Matrix Theory is not a good algebra textbook, but it is also a good book from the perspective of matrix skills.