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If we have two square matrices of the same size P and Q, we can put one in the exponent of the other by:

[tex] M = P^Q = e^{ln(P)Q} [/tex]

ln(P) may give multiple results R, which are square matrices the same size as P.

So then we have:

[tex] M = e^{RQ} [/tex]

which can be Taylor expanded to arrive at a final square matrix (matrices) M.

I've been wondering about this, and want to know if my approach is valid. Thank you.

Also, does anyone know any tricks in computing the log of a matrix?

If P is not diagonalizable, it seems you'd have to use the Taylor series expansion. So you'd have an expansion within an expansion for M.

[tex] M = P^Q = e^{ln(P)Q} [/tex]

ln(P) may give multiple results R, which are square matrices the same size as P.

So then we have:

[tex] M = e^{RQ} [/tex]

which can be Taylor expanded to arrive at a final square matrix (matrices) M.

I've been wondering about this, and want to know if my approach is valid. Thank you.

Also, does anyone know any tricks in computing the log of a matrix?

If P is not diagonalizable, it seems you'd have to use the Taylor series expansion. So you'd have an expansion within an expansion for M.

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