Orthonormalizes a set of vectors using the Gram-Schmidt process with the
Orthogonalize[{v1, v2, …}]
Orthogonalize[{e1, e2, …}, f]
Orthogonalize[{{3, 4}, {1, 0}}]
→ {{3/5, 4/5}, {4/5, -3/5}}Orthogonalize[{{1, 1}, {1, 0}}]
→ {{1/Sqrt[2], 1/Sqrt[2]}, {1/Sqrt[2], -(1/Sqrt[2])}}Orthogonalize[{{1, 2, 2}, {2, 1, 2}}]
→ {{1/3, 2/3, 2/3}, {10/(3*Sqrt[17]), -7/(3*Sqrt[17]), 2/(3*Sqrt[17])}}Orthogonalize[{{1, 1}, {2, 2}}]
→ {{1/Sqrt[2], 1/Sqrt[2]}, {0, 0}}Orthogonalize[{{1, 0, 0}, {0, 2, 0}, {0, 0, 3}}]
→ {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}