https://jorisbukala.com/tags/quaternion/ Recent content in Quaternion on Joris Bukala | Math & ML Hugo -- 0.153.4 en-us Thu, 09 Nov 2023 17:30:52 +0100 https://jorisbukala.com/posts/geometric-algebra/ Thu, 09 Nov 2023 17:30:52 +0100 https://jorisbukala.com/posts/geometric-algebra/ <h2 id="vector-product-aesthetics">Vector Product Aesthetics</h2> <h3 id="the-beauty-inner-product">The Beauty: Inner Product</h3> <p>Think back for a minute to your first Linear Algebra course: Remember how nice inner products were to compute? Try to think of how to do it off the top of your head. If it&rsquo;s a bit blurry: it&rsquo;s just taking each component of the vectors, multiplying them and adding all the results: $$\mathbf{a \cdot b} = \sum_{i=0}^{N} a_i b_i$$ Calculating it gives you a scalar that says something about the angle between the two. It is as simple to do in 687D as it is in 2D.</p>