Errata to " an Introduction to Hyperplane Arrangements " List of Additional Errata and Questions -i

• page 2: You speak of the “usual dot product”, but there is no “usual dot product” on a general finite-dimensional K-vector space. If you want to work in this generality, you should use the dual space. (Or else just identify V with Kn for this definition, or require the choice of a nondegenerate symmetric bilinear form V × V → K which is to serve as a dot product. I personally find it easier to invoke the dual space, because as soon as one introduces additional structures like a basis or a bilinear form, it starts clouding further definitions. Besides, you use linear forms in the next paragraph, even though in the next paragraph you actually use a basis!)