Root Systems and Lie Groups Quiz

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

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)

By scalar multiplication only

Through rotations in the space

By addition and subtraction

Through reflections in certain lines (correct)

<p>They provide a classification scheme for root systems</p> Signup and view all the answers

<p>Lie theory, algebraic groups, and spectral graph theory</p> Signup and view all the answers