A Hilbert Space is a mathematical concept used in various fields, including physics and engineering, to describe a complete and infinite-dimensional space. It extends the idea of Euclidean space, where we can visualize points and vectors, to more complex scenarios. In a Hilbert Space, we can work with functions and sequences, allowing for the analysis of quantum states in quantum mechanics. One of the key features of a Hilbert Space is the inner product, which helps define angles and distances between vectors. This property is essential for understanding concepts like orthogonality and projections, making it a fundamental tool in areas such as signal processing and machine learning.