Question

Let A be a square matrix such that A^3 = A. What can you say about the eigenvalues of A ?

Answer 1

I am actually not really sure :/ .

Answer 2

@wio

Answer 3

@tkhunny @waterineyes

Answer 4

My choices are:

The eigenvalues of a matrix A can only be λ = 0, or λ = − 1.


The eigenvalues of a matrix A can only be λ = 0, λ = 1, or λ = − 1.


The eigenvalues of a matrix A can only be λ = 1, or λ = − 1.


The eigenvalues of a matrix A can only be λ = 0.


The eigenvalues of a matrix A can only be λ = 1.


The eigenvalues of a matrix A can only be λ = 0, or λ = 1.

Answer 5

I really thought it was the last one.

Answer 6

http://www.cliffsnotes.com/study_guide/Determining-the-Eigenvalues-of-a-Matrix.topicArticleId-20807,articleId-20803.html

scroll down, i think it should be helpful ;)

Answer 7

@yummydum : No... I don't get it :/ .

Answer 8

http://en.wikipedia.org/wiki/Eigendecomposition_(matrix)

Eigendecomposition should give you a hint.

Answer 9

We haven't even learned that in class :/ .

Answer 10

:( .. well i dont know linear algebra i was just looking up stuff that could possibly help.. :\ hope you figure it out soon enough :)

Answer 11

Basically it has to have eigen values such that \[
\lambda ^3=\lambda
\]

Answer 12

This is true for \(0, 1,-1\)

Answer 13

Cube roots right... >.< . I forgot you can take the cube root of -1 >.< .

Answer 14

At least that is my understanding, I'm rusty on this topic.

Answer 15

It is correct :D . Thanks! I have to remember that cube roots are valid for negative numbers >.< .