Moore determinant over a division algebra

Well, let's start at the beginning. A determinant is a way to measure things about a matrix. A matrix is just a big grid of numbers. It can be 2x2 (that's like a square with 2 rows and 2 columns) or 3x3 or even bigger.

Now, imagine you have a special kind of matrix called a division algebra. This just means that you can do math operations like adding, subtracting, multiplying, and dividing with it.

The Moore determinant is a special formula that helps you figure out some things about this kind of matrix. It's named after a man named E.H. Moore who came up with the formula in the early 1900s.

This formula includes a bunch of different math operations like tr, det, and epsilon. Tr stands for trace, which is when you add up all the numbers on the diagonal of the matrix. Det stands for determinant, which is a fancy way of measuring things about the matrix. Epsilon is a letter in math that represents something called a permutation. That's when you switch around the order of the things in the matrix.

Now, the Moore determinant can tell you if a certain kind of math equation (called a polynomial) has a solution. It's kind of like asking if a puzzle has an answer. If the Moore determinant equals 0, then the equation doesn't have an answer. But if it doesn't equal 0, then the equation does have an answer.

So, in short, the Moore determinant is a formula that helps you figure out if a certain kind of math equation has a solution when you're using a special kind of matrix called a division algebra.