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As you did you can take the first vector v 1 as it is. So you first basis vector is u 1 = v 1 Now you want to calculate a vector u 2 that is orthogonal to this u 1. Gram Schmidt tells you that you

Orthogonal Projection Matrix Calculator. Projection onto a subspace.. P =A(AtA)−1At P = A ( A t A) − 1 A t. Rows: Columns: Set Matrix.