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Any function that can be expressed as a power series can be extended to apply to any algebra - that is, to any ring over a scalar field.

Thus if M is a square matrix then e

This doesn't work for vectors in general because there is no general multiply function with a vector result. (In 3D, you could try to apply it to the cross product, but it becomes rather uninteresting when raising any given vector to a power returns zero.)

If dealing with physical quantities, it will usually be the case that the argument (and result) will be dimensionless. But you could construct artificial situations. E.g. from F=ma you could write e

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