格拉姆-施密特正交化过程

GeoGebra 命令及参数

1. Vector(A) → e_1
2. Vector(B) → e_2
3. Vector(C) → e_3
4. Sequence(Max[0, Min[1, k - s]], s, 0, top - 1) → sl
5. Sequence(0 < sl(s) < 1, s, 1, top) → sc
6. Sequence(0 < sl(s) ≤ 1, s, 1, top) → sc'
7. MatrixRank(M) → cond
8. If(0 ≤ k ≤ 1, (B * (1 - k)) + (P1 * k), P1) → T1
9. If(1 ≤ k ≤ 2, (B * (1 - (k - 1))) + ((x(w2), y(w2), z(w2)) * (k - 1)), (x(w2), y(w2), z(w2))) → O1
10. Vector(B, O1) → Vec2
11. If(3 ≤ k ≤ 4, (C * (1 - (k - 3))) + (P2 * (k - 3)), P2) → T2
12. Segment(T1, B) → S1
13. Segment(T2, C) → S2
14. If(4 ≤ k ≤ 5, (C * (1 - (k - 4))) + (Q2 * (k - 4)), Q2) → O2
15. If(5 ≤ k ≤ 6, (Q2 * (1 - (k - 5))) + (P3 * (k - 5)), P3) → T3
16. Segment(T3, Q2) → S3
17. Vector((0, 0, 0), O2) → Vec3
18. If(6 ≤ k ≤ 7, (Q2 * (1 - (k - 6))) + (Q3 * (k - 6)), Q3) → O3
19. Vector((0, 0, 0), O3) → Vec4
20. OrthogonalPlane((0, 0, 0), Vector[pv31 ⊗ pv32]) → plane
21. Angle(w1, w2) → angle1
22. Angle(w2, w3) → angle2
23. Angle(w1, w3) → angle3
24. If(7 ≤ k ≤ 8, Vector[(w1 * (1 - (k - 7))) + (Nw1 * (k - 7))], w1) → K1
25. If(7 ≤ k ≤ 8, Vector[(w2 * (1 - (k - 7))) + (Nw2 * (k - 7))], w2) → K2
26. If(7 ≤ k ≤ 8, Vector[(w3 * (1 - (k - 7))) + (Nw3 * (k - 7))], w2) → K3
27. LaTeX(k, true, true) → text1
28. LaTeX(vall, true, true) → text2
29. Vector((0, 0, 0), O1) → w2'