This book takes for granted that readers have some previous knowledge of the calculus of real functions of one real variable. It would be helpful to also have some knowledge of linear algebra. However, for those whose knowledge may be rusty from long disuse or raw with recent acquisition, sections on the necessary material from these subjects have been included where appropriate. Although these revision sections (marked with the symbol ◊) are as self-contained as possible, they are not suitable for those who have no acquaintance with the topics covered. The material in the revision sections is surveyed rather than explained. It is suggested that readers who feel fairly confident of their mastery of this surveyed material scan through the revision sections quickly to check that the notation and techniques are all familiar before going on. Probably, however, there will be few readers who do not find something here and there in the revision sections which merits their close attention.
The current chapter is concerned with the fundamental techniques from linear algebra which we shall be using. This will be particularly useful for those who may be studying linear algebra concurrently with the present text.
Algebraists are sometimes neglectful of the geometric implications of their results. Since we shall be making much use of geometrical arguments, particular attention should therefore be paid to §1.3 onwards, in which the geometric relevance of various vector notions is explained.
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