Previous | Next --- Slide 36 of 42
Back to Lecture Thumbnails

Quaternions can be used to solve some of the limitations of transformation matrices in the real world, for instance, they can mitigate Gimbal Lock


The rotation properties of Complex numbers are of foundation importance for the Fast Fourier Transform. Complex numbers help transform the Slow or Naive Fourier Transform which runs in $\mathcal{O}(n^{2})$ time into the Fast variety that runs in $\mathcal{O}(n \cdot log(n))$ time.

Please See: Primitive Roots of Unity and Cooley-Tukey FFT.