# Tag Info

0

You really do need to read a lot of documentation, but perhaps this wil get you started. It will at least show you some the things you need to look up in the documentation. First, Mathematica works in radians, not degrees, so conversion to radians must be done. The degree sign (°) is the conversion factor (π/180). It can be typed by Esc+deg+Esc p = {250 ...

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Graphics3D[Arrow[{{0, 0, 0}, {Cos[60], Cos[60], -Cos[45]}}], PlotRange -> {#, #, #} &@{-1, 1}, Axes -> True, Boxed -> False, AxesOrigin -> {0, 0, 0}]

6

You are apparently looking for a way to reliably compare two numerical matrices by using their eigensystems. This can always be done for normal matrices by using the eigenvectors to construct their spectral decomposition. To do that, you shape the eigenvectors into the equivalent system of projectors. Then you can compare the projectors instead. The good ...

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This can be handled by Solve straightforwardly: r = RandomInteger[{-10, 10}, {2, 2}]; a = {{a1, 0}, {0, a2}}; b = {{b1, b2}, {b1, b2}}; c = {{c1, c1}, {c2, c2}}; Solve[r.a + b == c, {a1, a2, b1, b2, c1, c2}] {{a2 -> 18 a1, b2 -> -45 a1 + b1, c1 -> -9 a1 + b1, c2 -> 9 a1 + b1}} You can interpret this as saying that for any a1 and b1, the other ...

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Due to not having such a framework at hand, I used the following workaround, which allowed me to still shorten some computation time as compared to doing everything by hand. It boils down to having a set of conventions in place for how to write functions of arbitrarily many variables (or vectors or matrices of these). Here is a summary of the main ideas: ...

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V = {{176}, {648}}; MatrixForm[Mod[V, 26]]

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Ok, I'm not sure if I'm breaking any protocol by answering my own question but it wouldn't fit in the comments. I tried to work on the answers you guys gave in the comments. So I came up with the argument that DumpsterDoofus gave, creating a list that gives me the number of times that some specific combination of the coefficients shows up. list = ...

4

Other solutions are fine, but they use old MatrixConditionNumber as a magic box. However, it has a simple idea. The 2-norm condition number of the matrix $M$ is a ratio $\sigma_{\rm max}/\sigma_{\rm min}$ between the maximum and the minimum singular values. The maximum singular value $\sigma_{\rm max}$ can be estimated by a simple power iteration: ...

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