# Showing that something is in eigenspaceWatch

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#1
Let's say we have matrices X and Z which are both n x n matrices.

They have a property such that XZ = ZX

Let be an eigenvalue of X and it's eigenspace

1) Imagine that v 0 is element in
Show that Zv is also element of

Any help would be great.
0
5 years ago
#2
(Original post by Valentas)
Let's say we have matrices X and Z which are both n x n matrices.

They have a property such that XZ = ZX

Let be an eigenvalue of X and it's eigenspace

1) Imagine that v 0 is element in
Show that Zv is also element of

Any help would be great.
Well what does v as an element of tell you about its interaction with X?

And then how do you show Zv is an element of ? What does it mean?

It drops out very quickly.
1
#3
(Original post by ghostwalker)
Well what does v as an element of tell you about its interaction with X?

And then how do you show Zv is an element of ? What does it mean?

It drops out very quickly.
Thank you for hints. I managed to solve this. It was dead simple. I just needed to re-read the chapter and then apply knowledge from there.
0
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