X–Y–Z matrix

3-dimensional visualization of the Levi-Civita symbol

In mathematics, an X–Y–Z matrix is a generalization of the concept of matrix to three dimensions.

An X–Y–Z matrix [math]\displaystyle{ A }[/math] will thus have components [math]\displaystyle{ A_{i, j, k} }[/math] with

[math]\displaystyle{ 1 \le i \le M, \quad 1 \le j \le N, \quad 1 \le k \le P }[/math]

for some positive integers [math]\displaystyle{ M, N, P. }[/math]

Such matrices are helpful, for example, when considering grids in three dimensions, as in computer simulations of three-dimensional problems.

See also

• Cartesian coordinate system
• Sparse array
• Tensor