Multidimensional Matrix Mathematics: Multidimensional Matrix Transpose, Symmetry, Antisymmetry, Determinant, and Inverse, Part 4 of 6

摘要

This is the first series of research papers to define multidimensional matrix mathematics, which includes multidimensional matrix algebra and multidimensional matrix calculus. These are new branches of math created by the author with numerous applications in engineering, math, natural science, social science, and other fields. Cartesian and general tensors can be represented as multidimensional matrices or vice versa. Some Cartesian and general tensor operations can be performed as multidimensional matrix operations or vice versa. However, many aspects of multidimensional matrix math and tensor analysis are not interchangeable. Part 4 of 6 defines the multidimensional matrix algebra operations for transpose, determinant, and inverse. Also, multidimensional matrix symmetry and antisymmetry are defined.