The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+9 votes
507 views
If $A = \begin{pmatrix} 1 & 0 & 0 & 1 \\ 0 & -1 & 0 & -1 \\ 0 & 0 & i & i \\ 0 & 0 & 0 & -i \end{pmatrix}$ the matrix $A^4$, calculated by the use of Cayley-Hamilton theorem or otherwise, is ____
asked in Linear Algebra by Veteran (68.8k points)
retagged by | 507 views

1 Answer

+22 votes
Best answer

Let λ be eighen value

Characteristic polynomial is 

(1-λ)(-1-λ)(i-λ)(-i-λ)

=(λ2-1)(λ2+1)

4-1

Characteristic equation is λ4-1=0

According to Cayley Hamilton theorem every matrix matrix satisfies its own characteristic equation

So A4=I

 

answered by Veteran (33.9k points)
selected by

Related questions



Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

32,621 questions
39,267 answers
109,742 comments
36,656 users