Projective Hilbert space
Okay kiddo, let's imagine you have a big box of toys that you want to organize. But, there are some toys that are very similar to each other, and you want to put them together in a specific way.
This is kind of like a projective Hilbert space! It's a way of organizing vectors (which are like toys) in a way that makes it easier to see how similar they are.
In a regular Hilbert space, all the vectors have a specific length and direction, just like all your toys would have a specific shape and size. But sometimes, two vectors might have the same direction, but not quite the same length, kind of like two toys that are similar but not exactly the same.
In a projective Hilbert space, we group these similar vectors together to create something called a "ray." A ray is basically a line that goes on forever in both directions, kind of like a toy train track that you can keep adding pieces to.
So, in our toy box example, we might group all the cars together in one ray, all the dolls in another ray, and all the animal figures in a third ray. This way, it's easier to see which toys are similar to each other.
That's kind of how projective Hilbert space works - it helps us organize vectors that are similar to each other in a way that makes it easier to see their similarities.
This is kind of like a projective Hilbert space! It's a way of organizing vectors (which are like toys) in a way that makes it easier to see how similar they are.
In a regular Hilbert space, all the vectors have a specific length and direction, just like all your toys would have a specific shape and size. But sometimes, two vectors might have the same direction, but not quite the same length, kind of like two toys that are similar but not exactly the same.
In a projective Hilbert space, we group these similar vectors together to create something called a "ray." A ray is basically a line that goes on forever in both directions, kind of like a toy train track that you can keep adding pieces to.
So, in our toy box example, we might group all the cars together in one ray, all the dolls in another ray, and all the animal figures in a third ray. This way, it's easier to see which toys are similar to each other.
That's kind of how projective Hilbert space works - it helps us organize vectors that are similar to each other in a way that makes it easier to see their similarities.