This is an explanation about this game.
Rule of transformation
The numbers will be changed according to the following rules.
- Only the number 0,1,2,3 and 4 are used. Addition and multiplication of these numbers are defined as the remainder divided by 5 of the usual addition and multiplication.
- If the clicked cell’s row-index is i and column-index is j, plus 1 to the i-th row j-th column of the 3×3 identity matrix. Let this matrix be P.
- Multiple P from left side and multiple inverse matrix of P from right side.
It means that this is a transformation of 3×3 square matrix on F_5=Z/5Z.
The goal is to change the matrix to Jordan normal form.
Example
Example of matrix P when the left-upper cell is clicked.
Matrix Example 1
Example of matrix P when the middle-upper cell is clicked.
Matrix Example 2
This game is related to the theory of linear algebra about Jordan normal form.