Multidimensional Matrix Mathematics: Multidimensional Null and Identity Matrices and Multidimensional Matrix Outer and Inner Products, Part 3 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 3 of 6 defines the multidimensional null matrix and multidimensional identity matrix. Also, the multidimensional matrix algebra operations for outer product and inner product are defined.