Calculating exp[iMθ] for a Matrix M

Thread starter neelakash
Start date Jun 10, 2007
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Matrix

AI Thread Summary

To calculate exp[iMθ] for the matrix M, which is defined as [[0, 1], [1, 0]], the approach involves using the expansion of the exponential function. The expression can be rewritten as cos(Mθ) + i sin(Mθ). This method allows for the separation of real and imaginary components from the resulting matrix. The discussion suggests that this approach is a solid strategy for solving the problem. Overall, the focus is on applying the properties of matrix exponentiation effectively.

Jun 10, 2007

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?

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Jun 10, 2007

Mindscrape

That sounds like a good idea.

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