The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
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A Kronecker delta is a compact notation that indicates the equivalent of a dot product in vector notations. In this usage, it takes the form of a Greek letter delta with two subscripts which indicate that the components are to be multiplied if the subscripts are equal and thrown out if the subscripts are different. That is, the Kronecker delta notation indicates that the x-components should be multiplied together, the y-components should be multiplied together, and the product of x- and y-components should be ignored.
The Kronecker delta is not only used in vector equations, however. It can be used with a set of subscripted functions to indicate the orthogonality of that set. If an arbitrary set Kn of functions is orthogonal, then the integral of the product of those functions Km and Kl with their appropriate weighting function will equal the Kronecker delta with respect to l and m: 1 if l = m and 0 if l and m are not equal. This flexible notation can also be used to mean that only those functions which "match" or have the same subscripts should be considered in product, or that only repeated subscripts should be considered. It can indicate that, even if the products would otherwise not be zero, there are considerations that leave them out of the problem at hand. The Kronecker delta is not something that can be proven or disproven--it merely indicates, without a lot of excess verbiage, which of several potential components the mathematician is using.