A Matrix Question

Invisibility confuses me, too.

This might help....

http://www.mathstools.com/section/main/system_equations_solver#.UxvOm_ldWSo

Can e be raised to the power of a matrix? I'm a bit rusty on these things, but I thought the exponent had to be a dimensionless scalar.

Mathematics is not my strong suit....

http://en.wikipedia.org/wiki/Matrix_exponential

http://en.wikipedia.org/wiki/Scale_invariance

Yes, as long as it is a real, square matrix then it has a scalar value known as the determinant, the dimensions of which exist outside of the matrix.

OK thanks, trying to get my head round the Wiki article SolarEagle sent, but without much joy!

Good luck with those articles. Too many times they're written by academicians for academicians, not for those of us who have to put them to practical use. I was never very good at proofs, but I could "see" how the method/equations would be useful for "real" problems.

btw- OP's original problem statement is simply the "quick" way to "solve" the system of differential equations for N simultaneous equations in n variables, where N = n (the definition of a square matrix), with an initial condition (x(0)) equal to a constant C. I'll leave the actual proof to him/her.