Gram-Schmidt orthogonalization applet (original) (raw)

This applet is a calculator for the Gram-Schmidt orthogonalization process. Select the dimension of your basis, and enter in the co-ordinates. You can then normalize each vector (by dividing out by its length), or make one vector v orthogonal to another w (by subtracting the appropriate multiple of w). If you do this in the right order, you will obtain an orthonormal basis (which is when all the inner products v_i . v_j are 0 except for the diagonal inner products, which are 1). Note that there may be some roundoff errors since all numbers are truncated to 3 decimal places.

This applet was written by Kim Chi Tran.