Nilpotent Matrix

**sparky** · February 23rd 2011, 04:32 PM

Hi,

Is my working and answer to the following question correct?

Question: Show that matrix A is nilpotent and state the index of nilpotency k

$A = \begin {pmatrix} -2 & 1 \\ -4 & 2 \end {pmatrix}$

Definition of Nilpotent: A matrix A is said to be nilpotent if $A^k=0$ for some positive integer k. The smallest k is called the index of nilpotency for A

$A^2 = \begin {pmatrix} -2 & 1 \\ -4 & 2 \end {pmatrix}$ $\begin {pmatrix} -2 & 1 \\ -4 & 2 \end {pmatrix}$

$= \begin {pmatrix} 0 & 0 \\ 0 & 0 \end {pmatrix}$

A is nilpotent, k=2

**Ackbeet** · February 23rd 2011, 04:33 PM

Looks good to me!

**sparky** · February 23rd 2011, 04:38 PM

Thanks Ackbeet

**Ackbeet** · February 23rd 2011, 04:38 PM

You're welcome.

Thread: Nilpotent Matrix

LinkBack

Thread Tools

Display

Nilpotent Matrix

Similar Math Help Forum Discussions

Matrix of a Nilpotent Operator Proof

Nilpotent matrix Invertible matrix

Proving a Matrix Nilpotent

Giving an example of a nilpotent matrix

Nilpotent Matrix

Search Tags