Extensions of symmetric operators
Symmetric operators are like toys that can do cool tricks. They take some input, play with it and give you an output. Sometimes they can only play with certain types of input, but when they can, they are really good at it.
Now, what if we want to play with more types of input? Well, we can create new toys! We can make similar toys that can play with different types of inputs, and we call these new toys "extensions" of the original symmetric operators.
Think of it like you have a ball that you can throw really well, but you want to be able to throw other types of balls too, like a frisbee or a stuffed animal. You can't throw them with the same technique as the ball, but you can learn new techniques to throw them. These new techniques are like the extensions of the symmetric operators.
So, when we extend symmetric operators, we create new toys that can play with more types of input and still maintain the cool tricks of the original symmetric operator.
Now, what if we want to play with more types of input? Well, we can create new toys! We can make similar toys that can play with different types of inputs, and we call these new toys "extensions" of the original symmetric operators.
Think of it like you have a ball that you can throw really well, but you want to be able to throw other types of balls too, like a frisbee or a stuffed animal. You can't throw them with the same technique as the ball, but you can learn new techniques to throw them. These new techniques are like the extensions of the symmetric operators.
So, when we extend symmetric operators, we create new toys that can play with more types of input and still maintain the cool tricks of the original symmetric operator.