Curves and Surfaces from 3-D Matrices. Dan Dreibelbis University of North Florida. Richard. Goals. What is a 3-D matrix? Vector multiplication with a tensor Geometric objects from tensors Motivation Pretty pictures Richard’s work More pretty pictures. 3-D Matrices.
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University of North Florida
This is a tensor multiplication with two vectors!!
Two AEC are equivalent if there is a change of
coordinates that takes one form into another.
Goal: Find a representative of each equivalence class.
Theorem:Any nondegenerate 3x3x3 tensor is equivalent to a tensor of the form:
for some c and d. The AEC for this tensor is:
Theorem: For any nondegenerate 3x3x3 tensor, the AEC, BEC, and CEC are all projectively equivalent.
This is far from obvious: