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First question: See How can I overload a function with multiple bracket-slots so f[a][b] and f[a] can coexist?, and the comments. Second question: Without the s, C_ is a pattern which we can call C on the right hand side. (It seems like you understand this.) With the s included, C_s is likewise a pattern that we can call C, but it only matches ...


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The solution to your Eigenvalues function are Root objects, see the documentation. Root[f,k] represents the exact k^(th) root of the polynomial equation f[x]==0. Inside Root is the pure function in the argument #1. If we named this pure function f with argument x, this would correspond to the situation in the above quote with f[x]. Your Matrix $A$ ...



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