silemus.
← All examples
  1. 23×33\times 3 determinant expansion
  2. 10Eigenvalues of a 3×33\times 3 matrix
  3. 12Eigenvector for eigenvalue 3
  4. 14Inverse of a 2×22\times 2 matrix
  5. 17Solving a 3×33\times 3 linear system
  6. 20System with no solution
  7. 21Singular matrix, det=0
  8. 22Eigenvalue zero of a matrix
  9. 27Null space of a matrix
  10. 37Volume via scalar triple product
  11. 43Characteristic polynomial, 2×22\times 2
  12. 47Orthogonal matrix check
  13. 48Gram-Schmidt second vector
  14. 49Least-squares line fit
  15. 50Coordinates in a new basis
  16. 51Distance point to plane

48Gram-Schmidt second vector

Apply Gram–Schmidt to v1=(1,1,0)\displaystyle v_1 = (1, 1, 0), v2=(1,0,1)\displaystyle v_2 = (1, 0, 1). Find the second orthogonal vector u2\displaystyle u_2 before normalising.

Keep u1 = v1 = (1,1,0). Then u2 = v2 minus the part of v2 lying along u1: u2 = (1,0,1) − ½(1,1,0) = (½, −½, 1). Checking, u2·u1 = 0, so they're perpendicular.

How good is this answer?