# Minimal polynomial

## Homework Statement

Given the matrix
2 0 0 0 0 0 0
1 2 0 0 0 0 0
0 1 2 0 0 0 0
0 0 1 2 0 0 0
0 0 0 0 2 0 0
0 0 0 0 1 2 0
0 0 0 0 0 0 2

What is the minimal polynomial?

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## The Attempt at a Solution

This is the Jordan form, so I guess the solution is just m(t) = (t-2)7 but I don't know if it's right. Can anyone help me?

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Homework Helper

## Homework Statement

Given the matrix
2 0 0 0 0 0 0
1 2 0 0 0 0 0
0 1 2 0 0 0 0
0 0 1 2 0 0 0
0 0 0 0 2 0 0
0 0 0 0 1 2 0
0 0 0 0 0 0 2

What is the minimal polynomial?

-

## The Attempt at a Solution

This is the Jordan form, so I guess the solution is just m(t) = (t-2)7 but I don't know if it's right. Can anyone help me?

Hi cristina89! The minimal polynomial P of a square matrix A is the unique monic polynomial of least degree, m, such that P(A) = 0.

The degree of the minimal polynomial is determined by the size of the largest Jordan block, which is 4 in your case.
So the minimal polynomial is m(t) = (t-2)4.

Indeed ##(A-2I)^4=0##.

Thank you so much!! :)

Ray Vickson