In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras. Since Lie groups (and some analogues such as algebraic groups) and Lie algebras have become important in many parts of mathematics during the twentieth century, the apparently special nature of root systems belies the number of areas in which they are applied. Further, the classification scheme for root systems, by Dynkin diagrams, occurs in parts of mathematics with no overt connection to Lie theory (such as singularity theory). Finally, root systems are important for their own sake, as in graph theory in the study of eigenvalues.
Read more about Root System: Definitions and First Examples, History, Elementary Consequences of The Root System Axioms, Positive Roots and Simple Roots, Dual Root System and Coroots, Classification of Root Systems By Dynkin Diagrams, Properties of The Irreducible Root Systems, Root Systems and Lie Theory
Famous quotes containing the words root and/or system:
“But a cultivated man becomes ashamed of his property, out of new respect for his nature. Especially he hates what he has if he see that it is accidental,—came to him by inheritance, or gift, or crime; then he feels that it is not having; it does not belong to him, has no root in him and merely lies there because no revolution or no robber takes it away.”
—Ralph Waldo Emerson (1803–1882)
“For the universe has three children, born at one time, which reappear, under different names, in every system of thought, whether they be called cause, operation, and effect; or, more poetically, Jove, Pluto, Neptune; or, theologically, the Father, the Spirit, and the Son; but which we will call here, the Knower, the Doer, and the Sayer. These stand respectively for the love of truth, for the love of good, and for the love of beauty.”
—Ralph Waldo Emerson (1803–1882)