Why is the matrix organization structure described as a "violation of unity of command", and what follows from that?

Because every employee deliberately has two bosses — a functional head and a project manager — making conflict resolution a built-in design requirement.

The matrix is the realization of a two-dimensional structure emanating from two dimensions of authority:

• A project manager is appointed to coordinate each project
• Personnel are drawn from functional departments but stay attached to them
• Each person serves the administrative (functional) head and the project manager

Consequences:

• Merits: flexibility, end-result focus, preserved professional identity, resource accountability
• Demerits: needs much more coordination, authority & responsibility hard to define, demotivation risk when bosses conflict
• Works only with explicit conflict-resolution rules (who wins when functional and project priorities clash?)

Suitability: dual focus + heavy information processing + shared resources (aerospace, chemicals, banking, brokerage, advertising).

Tip: Ask of any matrix: "When my two bosses disagree, who decides?" If the answer is undefined, the matrix exists on paper only.

Go deeper:

• Matrixorganisation (Wikipedia DE) — Belegt den bewussten Verstoß gegen die Einheit der Auftragserteilung und die nötigen Konfliktlösungsregeln.
• Unity of command (Wikipedia) — the principle the matrix deliberately breaks.