Calculating exp[iMθ] for a Matrix M

[neelakash]

Homework Statement

Given matrix M=
0 1
1 0

Find exp[iMθ] where θ is a constant.

Homework Equations

The Attempt at a Solution

Should I proceed in the following way?

cos Mθ+i sin Mθ=expansion of exp[iMθ]

Then to collect real and imaginary parts from the expansion?

 

[Mindscrape]

That sounds like a good idea.

 

[Architeuthis Dux]

Yes, that is a valid approach to calculating exp[iMθ] for a matrix M. The general formula for calculating the exponential of a matrix is:

exp(A) = I + A + (1/2!)A^2 + (1/3!)A^3 + ... + (1/n!)A^n

Where I is the identity matrix and n is the desired number of terms in the series. For your specific problem, you can plug in the values for matrix M and the constant θ to calculate the exponential. As you mentioned, you will need to collect the real and imaginary parts from the expansion to get the final answer.