# Definition: Hilbert Space

A Banach space \((V,||~||)\), in which the norm \([||~||"\) is given by the square root \[||~||:=\sqrt{\langle\cdot,\cdot\rangle},\] where \(\langle\cdot,\cdot\rangle\) is a positive definite dot product is called a **Hilbert space**, named after the German mathematician David Hilbert (1862 - 1943).

Thank you to the contributors under CC BY-SA 4.0!

### References

#### Bibliography

**Wille, D; Holz, M**: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994