The vector and tensor case is more complicated because of the need to account for the change of basis vectors.

Source: Changing Coordinate Systems—Wolfram Language Documentation

The vector and tensor case is more complicated because of the need to account for the change of basis vectors.

Source: Changing Coordinate Systems—Wolfram Language Documentation

Source: Continued fraction – Wikipedia

How can one prove the following identity of the cross product? $$(M a)\times (M b)=\det(M) (M^{\rm T})^{-1}(a\times b)$$ $a$ and $b$ are 3-vectors, and $M$ is an invertible real 3×3 matrix.

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shear matrix or transvection

Source: Shear matrix – Wikipedia

ListPointPlot3D[{{x1, y1, z1}, {x2, y2, z2}, …}] generates a 3D scatter plot of points with coordinates {xi, yi, zi}. ListPointPlot3D[array] generates a 3D scatter plot of points with a 2D array of height values. ListPointPlot3D[{data1, data2, …}] plots several collections of points, by default in different colors.

I have this: f[x_, y_] = x y/(x^2 + y^2); ParametricPlot3D[{t, 2 t, f[t, 2 t]}, {t, -1/2, Sqrt[0.002]}, PlotStyle -> Directive[Red, Thick]] /. Line -> Tube Which works, but I would like an