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What is a root system in mathematics?
What is a root system in mathematics?
- A system of linear equations with multiple solutions
- A set of complex numbers satisfying certain algebraic properties
- A configuration of vectors in a Euclidean space satisfying certain geometrical properties (correct)
- A group of polynomials with a common root
What do the vectors in a root system do?
What do the vectors in a root system do?
- Always point in the same direction
- Form a basis for a subspace of the Euclidean space
- Are orthogonal to each other
- Span the whole space and have specific reflection properties (correct)
How are the vectors related in a root system?
How are the vectors related in a root system?
- By scalar multiplication only
- Through rotations in the space
- By addition and subtraction
- Through reflections in certain lines (correct)
What is the significance of Dynkin diagrams in the context of root systems?
What is the significance of Dynkin diagrams in the context of root systems?
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In which areas of mathematics are root systems applied?
In which areas of mathematics are root systems applied?
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