How to find the order of a matrix?

  • Thread starter xsw001
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  • #1
For example the Heisenberg group over Field.

H(F) is a 3x3 upper right triangle where the entries on the main diagonals are all 1's.

So by definition that I need to use this matrix and raise to the power where it becomes the identity matrix, then the number of that power would the order of H(F). But if I take the upper right triangle with all 1's in the main diagonal, it would never becomes identity matrix though no matter how many times I multiple them.

I couldn't find any examples from the material that I have. Am I doing something wrong here? Any suggestions?

Answers and Replies

  • #2
If you have [tex]g^m\ne1[/tex] for every positive integer m, you say that g has infinite order.