# Hautus lemma

In control theory and in particular when studying the controllability of a linear time-invariant system in state space form, the Hautus lemma, named after Malo Hautus, can prove to be a powerful tool. This result appeared first in [1] and.[2] Today it can be found in most textbooks on control theory.

## The main result

The Hautus lemma says that given a square matrix ${\displaystyle {\mathbf {A} }\in M_{n}(\Re )}$ and a ${\displaystyle {\mathbf {B} }\in M_{n\times m}(\Re )}$ the following are equivalent:

## References

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