Linear Algebra Interactive

Gram-Schmidt Vector Orthogonalizer

Drag input vector arrowheads (v₁, v₂) or step through projection subtraction Normalize Basis (û)

Geometric Presets

Input Vectors (v_k)

v₁

X: Y:

v₂

X: Y:

Pairwise Inner Products (u_i · u_j)

•	u₁	u₂
u₁	-	-
u₂	-	-

Gram-Schmidt Step Computation

Step 0: Initial Raw Vectors

u₁ = v₁
u₂ = v₂ - proj_u₁(v₂)

Status: Non-orthogonal input vectors.

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