Orthogonal Cycle Decomposition

Definition

The decomposition that carries content: the capital space splits orthogonally into the mission-aligned subspace and its complement. E is the residue left by the alignment operator — K = A(K) + E(K) holds of any operator at all and is not the result.

Formula

Example

A hospital's capital behaviour projects onto the equipment-cycle-matched subspace; what is left over is budget-cycle driven. The orthogonality is what makes the split unique — additivity alone would not.

Source

OAIA §3 (decomposition)