Exploring the Unseen: Degrees of Freedom in 4D Rotation
<p>When discussing rotation, it’s fundamentally about altering our viewpoint or perspective to observe objects differently. But what makes rotational transformation special? It preserves the structure of space. In mathematical terms, any vector in space maintains its length after the transformation.</p>
<p>In linear algebra language, let’s suppose <em>v</em> is a vector, and <em>v</em>′ is the transformation of <em>v</em> after applying rotational transformation. Calculating the length involves taking the dot product of the vector with itself:</p>
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