Chapter 8: Our Space in the Universe
Our space in the universe is called a Hilbert space. A Hilbert space is a type of vector space that has certain properties – properties that we will develop in this chapter. The most important will be defining an inner product. Once this is done, we will be able to measure distance and angles between vectors in an n-dimensional complex space. We will also be able to measure the length of vectors in these spaces. Later in the chapter, we will look at putting these Hilbert spaces together into even bigger Hilbert spaces through the tensor product!
The other main topic of this chapter is linear operators. We will go through many types, showing the distinct properties of each.
In this chapter, we are going to cover the following main topics:
- The inner product
- Orthonormality
- The outer product
- Operators
- Types of operators
- Tensor products
