X–Y–Z matrix

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

3-dimensional visualization of the Levi-Civita symbol

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

${\displaystyle 1\leq i\leq M,\quad 1\leq j\leq N,\quad 1\leq k\leq P}$

for some positive integers ${\displaystyle M,N,P.}$

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