a.) Find a singular value decomposition for X = 1-1 11
b.) Find a reduced singular value decomposition for the matrix X in part a.
Question & Answer
Please answer A and B question 3 a. Find singular value decomposition b. Find a reduced singular value decomposition for the matrix x
1 Answer
Verified archive- The SVD factors the matrix X into three components: U, Σ, and V^T.
- U is a 3×3 orthogonal matrix containing the left singular vectors.
- Σ is a 3×2 diagonal matrix containing the singular values (4.2426 and a very small value treated as 0).
- V^T is a 2×2 orthogonal matrix containing the right singular vectors.
- For the reduced SVD, only the largest singular value (4.2426) and its corresponding vectors in U and V are kept.
- This provides a rank-1 approximation to the original matrix X.