SVD of a 2x2 Matrix
Decomposition & Spectral Methods DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding Singular Value Decomposition (SVD) for 2x2 Matrices, Frobenius Norm, Principal Component Analysis (PCA) basis, Rotation and Scaling transformations, Condition Number computation, Unitary Transformation, Linear Algebra, Matrix Calculus, Numerical Analysis, Spectral Theory, Dimensionality Reduction, Orthogonal Matrices, Eigenvalue Decomposition, Singular Values, Matrix Factorization, Vector Spaces.
Implement a function that performs Singular Value Decomposition on a 2x2 matrix A. The function should return the matrices U, S (as a vector of singular values), and V T such that A = U diag(S) V T. Ensure the singular values are returned in descending order.