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arkadiusz-jadczyk.eu | ||
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nbodyphysics.com
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| | | | | My Unity asset Gravity Engine models orbits around planets. These are typically ellipses so gravity engine generates a lot of ellipses. The simplest way to do this is to use an equation for the ell... | |
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codethrasher.com
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| | | | | A linear mapping from a vector space to a field of scalars. In other words, a linear function which acts upon a vector resulting in a real number (scalar) \begin{equation} \alpha\,:\,\mathbf{V} \longrightarrow \mathbb{R} \end{equation} Simplistically, covectors can be thought of as "row vectors", or: \begin{equation} \begin{bmatrix} 1 & 2 \end{bmatrix} \end{equation} This might look like a standard vector, which would be true in an orthonormal basis, but it is not true generally. | |
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nhigham.com
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| | | | | Various explicit parametrized formulas are available for constructing orthogonal matrices. To construct a random orthogonal matrix we can take such a formula and assign random values to the parameters. For example, a Householder matrix $latex H = I - 2uu^T/(u^Tu)$ is orthogonal and symmetric and we can choose the nonzero vector $latex u$ randomly. Such... | |
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francisbach.com
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