Positive linear operator

Okay kiddo, so imagine you have a machine that takes in numbers and gives out other numbers. A positive linear operator is a type of machine that always gives out a number that is bigger than or equal to zero, no matter what number you put in.

Let's say you put the number 3 into the machine. The positive linear operator will do some math with that number (like add or multiply it by another number) and then give you a new number. That new number will always be 0 or bigger.

Now imagine you put in a different number, like -2. The positive linear operator will do the same type of math with that number and still give you a new number that is 0 or bigger.

So basically, a positive linear operator is a machine that always gives out non-negative (meaning not less than zero) numbers no matter what number you put in. Pretty cool, huh?