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Matrix exponentiation watch

1. Hi Guys,

I have a matrix which I need to exponentiate. I have dy/dt=By
and I solved to obtain, y=exp(Bt)y_0, I cannot perform a similarity transformation to obtain a diagonal matrix similar to B as it will yield complex diagonal entries. How do I obtain exp(Bt)?

Any help will be appreciated,

2. (Original post by tsmith16)
Hi Guys,

I have a matrix which I need to exponentiate. I have dy/dt=By
and I solved to obtain, y=exp(Bt)y_0, I cannot perform a similarity transformation to obtain a diagonal matrix similar to B as it will yield complex diagonal entries. How do I obtain exp(Bt)?

Any help will be appreciated,

As B is a rectangular matrix I think y is a vector of function y=(y_1(t), y_2(t) ...)
So you have a differential equation system to solve, If I think right.
There is a proved method for solving these type of systems
(depending on eigen values and vectors of B they will be different functions containing exponential functions as part of the solution)
3. You can still use a similarity transform even if you get complex eigenvalues. (And in fact this is exactly what you'll need to do).

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