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Book: RootSystemsArePositiveDefinite


See: Math notebook

What does it mean that root systems are positive definite?



Root systems describe the Lie algebra, which explains the "flat part" of the Lie group, thus the positive definite component in the polar decomposition.

The Cartan matrix expresses the amount of slack in the root system, so that you can move from the tip of one vector by X steps with another vector and stay within the root system.

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Puslapis paskutinį kartą pakeistas 2019 rugsėjo 24 d., 15:53