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nulliq.dev | ||
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www.scijournal.org
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| | | | | This guide will show you how to write a dot product in LaTeX | |
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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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austinmorlan.com
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| | | | | It took me longer than necessary to understand how a rotation transform matrix rotates a vector through three-dimensional space. Not because it's a difficult concept but because it is often poorly explained in textbooks. Even the most explanatory book might derive the matrix for a rotation around one axis (e.g., x) but then present the other two matrices without showing their derivation. I'll explain my own understanding of their derivation in hopes that it will enlighten others that didn't catch on right away. | |
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marc-b-reynolds.github.io
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| | | using visualizating as an exercise to note some quaternion properties | ||
