Matrix Factorization Structure

A Matrix Factorization Structure is a matrix structure that decomposes an [math]\displaystyle{ m \times n }[/math] matrix [math]\displaystyle{ X }[/math] into a product of matrices (in some canonical form) - typically into [math]\displaystyle{ m×k }[/math] and [math]\displaystyle{ k×n }[/math] matrices, where typically [math]\displaystyle{ k \ll n }[/math] and [math]\displaystyle{ k \ll m }[/math].

• AKA: Matrix Decomposition Structure.
• Context:
  • It can be produced by a Matrix Factorization System (that is solving a matrix factorization task).
• Example(s):
  • a QR Decomposition Structure.
  • an SVD Structure.
• See: Orthonormal Matrix.

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