Hilbert spaces are a fundamental concept in mathematics, particularly in functional analysis and quantum mechanics. They are a type of abstract vector space that extends the notion of Euclidean spaces to infinite dimensions and incorporates concepts from linear algebra and calculus. ### Key Features of Hilbert Spaces: 1. **Vector Space**: A Hilbert space is a complete vector space, meaning it has all the properties of a vector space (such as closure under addition and scalar multiplication).
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