Positive operator (Hilbert space)
A positive operator in a Hilbert space is like having a big box of toys to play with. Imagine you have a toy box full of different kinds of toys. Some are big, some are small, some are soft, and some are hard. Now, imagine that you have a special friend who helps you pick out the toys that you like the most. This friend only picks out the toys that are nice and friendly, and leave behind the toys that are mean or scary.
Well, in a Hilbert space, we have this special friend too! But instead of toys, we have mathematical things called operators. These operators are like little machines that take in some numbers or functions and spit out some other numbers or functions. Just like toys, some operators are nice and friendly, and some are not.
Our special friend, the positive operator, only likes to pick out the nice and friendly operators to play with. The nice and friendly operators are ones that behave well and make sense, just like the nice toys in your toy box. The not so nice operators are ones that are too complicated or don't make sense, just like the scary toys in your toy box.
So, in summary, a positive operator in a Hilbert space is like a special friend that only likes to pick out the nice and friendly operators to play with, leaving behind the not so nice ones. It's like having a toy box full of only the toys you like the most!
Well, in a Hilbert space, we have this special friend too! But instead of toys, we have mathematical things called operators. These operators are like little machines that take in some numbers or functions and spit out some other numbers or functions. Just like toys, some operators are nice and friendly, and some are not.
Our special friend, the positive operator, only likes to pick out the nice and friendly operators to play with. The nice and friendly operators are ones that behave well and make sense, just like the nice toys in your toy box. The not so nice operators are ones that are too complicated or don't make sense, just like the scary toys in your toy box.
So, in summary, a positive operator in a Hilbert space is like a special friend that only likes to pick out the nice and friendly operators to play with, leaving behind the not so nice ones. It's like having a toy box full of only the toys you like the most!