Christian Rau
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 Feb 2 comment Multiplying double-centered matrix to a unit vector @user506901 And when $D$ is orthogonal (or more precisely orthonormal) it doesn't change the length of a vector and thus corresponds to a rotation (if $\det Q=1$) or a reflection (if $\det Q=-1$) around the origin. Feb 2 comment Multiplying double-centered matrix to a unit vector @user506901 Ah, that's what you mean by translation (never heard of such a definition for translation, but Ok). But I'm not sure if that is done by a general double-centred matrix. So you mean centering means adding a constant to all its entries? Well in this case, like said, I'm not sure this is achieved by multiplying by a general double-centred matrix. I thought you mean a vector whose element sum is $0$, like in your definition of a double-centred matrix. Maybe you can add this definition to the question (maybe along with what you think is a translation of a vector). Feb 1 awarded Critic Feb 1 comment Finding inverse of a $3\times 4$ or $4\times 3$ matrix But it is still not an answer to the general question "How would you calculate inverse of such a matrix?", instead if your answer was "by using WolframAlpha". In this case it would just be a bad answer. Feb 1 revised Multiplying double-centered matrix to a unit vector deleted 48 characters in body Feb 1 revised Multiplying double-centered matrix to a unit vector deleted 48 characters in body Feb 1 answered Multiplying double-centered matrix to a unit vector Feb 1 comment Minimizing the matrix norm, equivalence @user506901 Aah! So that's what's missing from your question. Now add it in, as otherwise Sam's answer in the correct one, of course. Feb 1 revised Minimizing the matrix norm, equivalence fixed formatting Feb 1 comment Minimizing the matrix norm, equivalence But in this case your matrix $X$ probably has to suffice some additional criteria. As otherwise you could just take $X=C$, which makes both norms $0$, the most minimal minimum that can be achieved. So like Sam said, not every $X$ that minimizes the first equation needs to minimize the second. But we need to know the constraints imposed on $X$ (by the external algorithm or whatever), as I guess you cannot just set $X=C$. Feb 1 suggested approved edit on Minimizing the matrix norm, equivalence Feb 1 awarded Citizen Patrol Jan 31 comment Rotating between $3$D frames The ambiguity doesn't only occur at singularities. Every rotation can be represented by at least two different Euler angle-triples, because $(x,y,z)$ and $(x\pm\pi,\pi-y,z\pm\pi)$ result in the same rotation. Jan 31 revised Minimizing the matrix norm, equivalence fixed terminology Jan 31 suggested approved edit on Minimizing the matrix norm, equivalence Jan 31 revised Minimizing the matrix norm, equivalence corrected formatting Jan 31 suggested approved edit on Minimizing the matrix norm, equivalence Jan 30 comment Generating orthogonal axes on a spline @John Don't know. It never was a problem for me. If I ever need C2 continuity on the whole curve, I just take a cubic B-Spline. Otherwise you just have to be sure to restrict the relevant interval to a single spline in every computation that needs a continuous 2nd derivative (e.g. Newton-based minimization or examination of curvature development). Jan 30 revised Generating orthogonal axes on a spline added 54 characters in body Jan 30 answered Generating orthogonal axes on a spline