Orthogonalize

Orthogonalize[{v1, v2, ...}] gives an orthonormal basis found by orthogonalizing the vectors vi.

Examples

Orthonormalize vectors:

Orthogonalize[{{1, 0, 1}, {1, 1, 0}, {0, 1, 1}}]
(* {{1/Sqrt[2], 0, 1/Sqrt[2]}, {1/Sqrt[6], Sqrt[2/3], -1/Sqrt[6]}, ...} *)

Simple 2D example:

Orthogonalize[{{1, 1}, {1, 0}}]
(* {{1/Sqrt[2], 1/Sqrt[2]}, {1/Sqrt[2], -1/Sqrt[2]}} *)

Please visit the official Wolfram Language Reference for more details.