Artificial Intelligence for Big Data

The important properties of singular value decomposition

Now, let's take a look at some of the important properties of SVD:

• It is always possible to decompose a real matrix A into 
• U, ∑, and V are unique
• U and V are orthonormal matrices:
  • U^TU = I and V^TV = I (I represents an identity matrix)
• ∑ is a diagonal matrix where the nonzero diagonal entries are positive and sorted in descending order (σ₁ ≥ σ₂ ≥ σ₃....≥σ_n....>0)