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I have twelve 4x4 matrices with specific complex-valued entries. I would like to know if they are linear independent over the reals. Is there some feature of Maple that enables me to do that easily? I've tried adding together all the matrices, each separately multiplied by an unspecified algebraic number, and then to use solve(). But I don't trust the result, partly because it becomes rather tedious, partly because the package RealDomain, with which I've no experience, has to be invoked in order to avoid producing a false solution of linear dependence over the complex numbers. I've also tried defining a 12x12 matrix consisting of bilinear traces of the matrices, analogous to the Cartan matrix in Lie algebra theory, and then taking the determinant to test for degeneracy. This actually gives zero determinant, but I suspect it to be a false linear dependence over the complex numbers, not the reals.
algebra complex package linear

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