GraphMath

Projection

From one direction to a subspace: orthogonal projection in vector and matrix form

Understand projection from its simplest vector form to the matrix formula for projection onto a column space. This chapter develops orthogonal projection onto one direction and onto the columns of a matrix, compares orthogonal and general projection and derives the idempotency of the projection matrix.

Chapter contents

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Topic Pages
Orthogonal projection of vector v⃗ on direction of vector u⃗ 1
Orthogonal projection of vector v⃗ on columns of U = [ u⃗₁, u⃗₂, ..., u⃗ᵣ ] 1–3
Orthogonal vs general projection (optional reading) 4–7
Idempotency of P 7–8

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