004 Vandermonde Matrix

99 CENT SPECIAL
Start Here:
chatGPT image and text prompt at www.wickersonstudios.com
Creating an interesting 3D geometry to visualize the data from a Vandermonde matrix involves interpreting the mathematical properties of the matrix in a spatial context. Here's a conceptual approach to visualize a Vandermonde matrix in 3D using Grasshopper and Rhino:
Points Representation: Each row of the matrix could be represented by a series of points in space, where the horizontal position corresponds to the column index and the vertical position corresponds to the value of α raised to the power of the column index.
Curves or Surfaces: Interpolating curves through the points of each row could visualize the progression of powers for each α. Alternatively, lofted surfaces between these curves could create a continuous surface representing the entire matrix.
Color Mapping: The determinant expression could be visualized by mapping colors to the geometry based on the value of the determinant for subsets of the matrix. This would require calculating the determinant of smaller matrices formed by choosing subsets of rows. (Det included, Color Mapping not included)
Here is a more detailed C# script for Grasshopper that outlines this approach: