The Column-Row (CR) factorization expresses a matrix as:

$ A = CR $

where:

• $C$ is an $m \times r$ matrix containing the linearly independent columns of $A$
• $R$ is an $r \times n$ matrix containing the nonzero rows of RREF$(A)$
• $r = \text{rank}(A)$

How it works:

1. Compute RREF$(A)$ to identify pivot columns
2. $C$ = columns of $A$ corresponding to pivot positions
3. $R$ = nonzero rows of RREF$(A)$

Applications:

• Reveals the rank and basis for column space
• Efficient storage for low-rank matrices
• Understanding matrix structure and dependencies