About Jordan normal form game

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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

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: ,