
Be the first to like this
Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.
Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.
Published on
Proceedings  NCUR X. (1996), Vol. II, pp. 994998 Jeffrey F. Gold Department of Mathematics, Department of Physics University of Utah Don H. Tucker Department of Mathematics University of Utah Introduction The purpose of these remarks is to introduce a variation on a theme of the scalar (inner, dot) product and establish multiplication in R^{n}. If a = (a_{1},...,a_{n}) and b = (b_{1},...,b_{n}), we define the product ab = (a_{1}b_{1},...,a_{n}b_{n }). The product is the multiplication of corresponding vector components as in the scalar product; however, instead of summing the vector components, the product preserves them in vector form. We define the inner sum (or trace) of a vector a = (a_{1},...,a_{n}) by (a) = a_{1}+...+a_{n}. If taken together with an additional definition of cyclic permutations of vectors, we are able to prove complicated vector products (combinations of dot and cross products) extremely efficiently, without appealing to the traditional (and cumbersome) epsilonijk proofs. When applied to determinants, this method hints at the rudiments of Galois theory.
Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.
Be the first to comment