The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+11 votes
573 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 (59.4k points)
retagged by | 573 views
+2

This might help ....

1 Answer

+24 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 Boss (31.3k points)
selected by
0
Cayley Hamilton theorem is very useful to find (1) Inverse of given matrix

                                                                           (2) Higher power of given matrix

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

34,770 questions
41,730 answers
118,876 comments
41,381 users