Ordinary differential equations involving matrices

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SUMMARY

The discussion centers on solving ordinary differential equations (ODEs) involving matrices with eigenvalues e = -1, e = i, and e = -i, each having a multiplicity of 1. The hint provided suggests that the system can be expressed in a basis where the equations take the form x' = -x, y' = iy, and z' = -iz. This indicates a clear pathway to solving the ODEs by separating the real and imaginary components of the solutions.

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  • Understanding of eigenvalues and eigenvectors in linear algebra
  • Familiarity with ordinary differential equations (ODEs)
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  • Experience with matrix exponentiation techniques
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ricky786
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hi i got the eigen values as e=-1, e=i, -i as the imaginary roots and both 1 multiplicities can some one complete the question please

thanks
 

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Welcome to PF!

Hi ricky786! Welcome to PF! :smile:
ricky786 said:
hi i got the eigen values as e=-1, e=i, -i as the imaginary roots and both 1 multiplicities can some one complete the question please

thanks

Hint: If the eigenvalues are -1 and ±i, then there's a basis in which x' = -x, y' = iy, z' = -iz …

now solve. :wink:​
 

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