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Tips on using your textbook
(Friedberg, Insel, and Spence)

The book's notation for the set of real numbers is $R$ rather than ${\bf R}$ ; for the complex numbers it is $C$ rather than ${\bf C}$ .
Whenever the book refers to a field $F$ , you may assume $F ={\bf R}$ unless otherwise specified. (Later in the course there may be times when we want to allow $F = {\bf C}$ .)
Note that the authors use the non-italic numeral "0" for the scalar ( i.e. number) 0, and an italic 0 for the zero element of a vector space. If you read carefully and the book has no typos, there should never be any confusion about whether something is the zero scalar or the zero vector.
Unless otherwise stated by the authors, lower-case letters near the end of the alphabet, such as $u,v,w,x,y,z$ , stand for vectors (elements of vector spaces), while lower-case letters near the beginning of the alphabet ( $a,b,c,$ etc.) stand for scalars. The authors do not seem to mention this explicitly.
The book has a notation index ("List of Symbols"). In the hardcover edition this three-page index is on the inside front cover, first page, and last page.