### What does **root system** mean?

# Definitions for root system

root sys·tem

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **root system**.

### Princeton's WordNet

rootage, root systemnoun

a developed system of roots

### Wikipedia

Root system

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, especially the classification and representation theory of semisimple 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 spectral graph theory.

### ChatGPT

root system

A root system is a configuration of vectors in a Euclidean space that satisfies certain geometric properties. It is often used in the study of Lie groups, Lie algebras, and algebraic geometry. The vectors in a root system, known as roots, are used to describe the structure of certain algebraic objects. The root system must satisfy three conditions: 1. It is invariant under reflection through hyperplanes orthogonal to the roots. 2. The only scalar multiples of a root that are themselves roots are the root itself and its negative. 3. For any two roots, the vector obtained by projecting the first onto a line orthogonal to the second is itself a root or the zero vector.

### Wikidata

Root system

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 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. Finally, root systems are important for their own sake, as in graph theory in the study of eigenvalues.

### Matched Categories

### Numerology

Chaldean Numerology

The numerical value of root system in Chaldean Numerology is:

**4**Pythagorean Numerology

The numerical value of root system in Pythagorean Numerology is:

**7**

### Examples of root system in a Sentence

Tryon Fire Chief Geoffrey Tennant:

It is a freak of nature, i think it was a matter of the tree

**root system**had failed and the tree came down.Tryon Fire Chief Geoffrey Tennant:

I think it was a matter of the tree

**root system**had failed and the tree came down.We made the determination to start nurturing these root suckers so that in the future we would have a new tree, it's still the same

**root system**, the same tree growing within that location.

## Translations for **root system**

### From our Multilingual Translation Dictionary

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