##  [Kronecker's Approximation Theorem](/kroneckers-approximation-theorem) 

  ##  [Kronecker's Approximation Theorem](https://puremath.quantumdictionary.io/kroneckers-approximation-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A theorem characterizing when linear combinations of real numbers with integer coefficients are dense modulo 1 in a torus: if 1, α1,...,αn are linearly independent over Q then the set of vectors (mα1 mod 1, ..., mαn mod 1) for m∈Z is dense in the n-torus; more generally it describes density of the subgroup generated by given real vectors modulo 1 under rational independence conditions.