scholarly journals Multidimensional matrices uniquely recovered by their lines

2013 ◽  
Vol 438 (5) ◽  
pp. 2430-2437
Author(s):  
Joon Yop Lee
Keyword(s):  
Multidimensional Matrices

A MULTIPLICATIVE DETERMINANT FOR 2m-DIMENSIONAL MATRICES

2013 ◽  
Vol 13 (01) ◽  
pp. 1350067 ◽  
Author(s):  
PAUL SUNDHEIM
Keyword(s):  
Higher Dimensions ◽  
Hypercomplex Numbers ◽  
Zero Divisors ◽  
Multidimensional Matrices

A multiplication for a specific nested collection of multidimensional matrices is defined by association with a system of n = 2m-dimensional hypercomplex numbers. A totally symmetric and multiplicative determinant is then derived from the system which extends the Cayley hyperdeterminant to these higher dimensions. The determinant is related to the zero divisors of the system of hypercomplex numbers. Properties of the determinant are then discussed.

scholarly journals Extremal functions of forbidden multidimensional matrices

2017 ◽  
Vol 340 (12) ◽  
pp. 2769-2781 ◽  
Author(s):  
Jesse T. Geneson ◽  
Peter M. Tian
Keyword(s):  
Extremal Functions ◽  
Multidimensional Matrices
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