Quadratic Jordan algebra
Okay, so remember when you learned about numbers and how they can be added and multiplied? Well, sometimes we have bigger things we want to add and multiply, like matrices (which are like boxes of numbers).
Now, a quadratic Jordan algebra is a special kind of algebra where we have matrices that follow certain rules. They have to be symmetric (which means if you draw a line down the middle, one side is a mirror image of the other) and they have to be "multiplicative" (which means when we multiply two of the matrices together, we get another matrix that follows these same rules).
These matrices also have a special number inside called the "trace" which is just the sum of the numbers on the diagonal. For a quadratic Jordan algebra, this trace has to follow a certain rule too, but we won't get into that right now.
Basically, a quadratic Jordan algebra is a special way of doing math with matrices that follow certain rules so we can study them more easily.
Now, a quadratic Jordan algebra is a special kind of algebra where we have matrices that follow certain rules. They have to be symmetric (which means if you draw a line down the middle, one side is a mirror image of the other) and they have to be "multiplicative" (which means when we multiply two of the matrices together, we get another matrix that follows these same rules).
These matrices also have a special number inside called the "trace" which is just the sum of the numbers on the diagonal. For a quadratic Jordan algebra, this trace has to follow a certain rule too, but we won't get into that right now.
Basically, a quadratic Jordan algebra is a special way of doing math with matrices that follow certain rules so we can study them more easily.