About Jordan normal form game

This is an explanation about this game.

Rule of transformation

The numbers will be changed according to the following rules.

  1. 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.
  2. 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.
  3. 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 of matrix P when the left-upper cell is clicked.

Matrix Example 1

Matrix Example 1


Example of matrix P when the middle-upper cell is clicked.

Matrix Example 2

Matrix Example 2


This game is related to the theory of linear algebra about Jordan normal form.

Category: 数学 | Tags: ,