Tensor product of Hilbert spaces
Okay kiddo, so you know what a Hilbert space is? It's like a special kind of space where we can talk about lots of different kinds of math things.
But sometimes, we want to put two Hilbert spaces together to make a new, bigger one. And that's where the tensor product comes in. It's like taking two toys and combining them to make a new, bigger toy.
But instead of combining them by putting them side by side or on top of each other, we're going to combine them by doing some special math stuff.
First, we take all the possible pairs of things we can get from the two Hilbert spaces. Then, we use this math trick called a tensor product to combine them in a fancy way.
It's like taking all the Lego blocks you have and building them together with all the Duplo blocks. But instead of just putting them next to each other, we're going to use this special glue that sticks them together in a really cool way.
This new, bigger Hilbert space we get from combining the two original ones is really useful for lots of different kinds of math problems. It's like having a new toy that can do lots of cool things the original two toys couldn't do on their own.
But sometimes, we want to put two Hilbert spaces together to make a new, bigger one. And that's where the tensor product comes in. It's like taking two toys and combining them to make a new, bigger toy.
But instead of combining them by putting them side by side or on top of each other, we're going to combine them by doing some special math stuff.
First, we take all the possible pairs of things we can get from the two Hilbert spaces. Then, we use this math trick called a tensor product to combine them in a fancy way.
It's like taking all the Lego blocks you have and building them together with all the Duplo blocks. But instead of just putting them next to each other, we're going to use this special glue that sticks them together in a really cool way.
This new, bigger Hilbert space we get from combining the two original ones is really useful for lots of different kinds of math problems. It's like having a new toy that can do lots of cool things the original two toys couldn't do on their own.