Gram-Schmidt Process in Three Dimensions

step

1

2

3

4

5

6

show axes

change the vectors

u

1

= {2,2,0},

u

2

= {2,4,1},

u

3

= {4,-4,4}

The Gram–Schmidt process converts a set of linearly independent vectors to a set of orthonormal vectors. This Demonstration illustrates the process in three dimensions with several steps. The original vectors

u

i

,

i=1,2,3

are converted to a set of orthogonal vectors

v

i

by subtracting appropriate projections. These vectors are then normalized to a set of orthonormal vectors

q

i

.