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    "## SVD pseudo inverse\n",
    "\n",
    "The pseudoinverse gives a “least squared error, minimum-norm” solution: Out of all $\\dot{q}$ vectors at your current $q$, the vector \n",
    "\n",
    "$$\\dot{q}_{s} = J^{+}(q)\\dot{p}_{\\text{in}}$$\n",
    "\n",
    "satisfies two conditions:\n",
    "\n",
    "1. Least squared error: There is no $\\dot{q}$ vector which will get closer to $\\dot{p}$ when passed through $J(q)$. (I.e. for $\\dot{p}_{s} = J(q)\\dot{q}_{s}$, the normed difference $\\lvert \\dot{p}_{\\text{in}}-\\dot{p}_{s} \\rvert$ is smaller than any other $\\lvert \\dot{p}_{\\text{in}} - \\dot{p} \\rvert$.\n",
    "\n",
    "2. Minimum-norm: Out of all $\\dot{q}$ that satisfy the first condition, $\\dot{q}_{s}$ is the smallest of those vectors. (I.e. $\\lvert \\dot{q_{s}}\\rvert$ is smaller than $\\lvert \\dot{q} \\rvert$ for all $\\dot{q}$ that minimize error in $\\dot{p}$.\n",
    "\n",
    "At the singularity, the set of achievable velocities loses one dimension (so that there are $\\dot{p}$ that cannot be exactly produced by a $\\dot{q}$), but for any $\\dot{p}_{\\text{in}}$ there is a set of $\\dot{q}$ that all come equally close to producing $\\dot{p}_{\\text{in}}$, and the pseudoinverse picks the smallest (in $\\dot{q}$-space) of these vectors."
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