Singular Value Decomposition (SVD) of 2x2 Matrix
Decomposition & Spectral Methods DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding the Geometric and Algebraic Decomposition of 2x2 Matrices, Singular Value Spectrum, Left Singular Vectors (U), Right Singular Vectors (V), Spectral Radius, Condition Number Calculation, Linear Algebra, Matrix Factorization, Numerical Analysis, Vector Spaces, Transformations, Orthogonal Matrices, Eigenvalues and Eigenvectors, Norms and Inner Products, Geometric Transformations, Rank-Deficient Matrices.
Given a 2x2 matrix A, compute its Singular Value Decomposition A = UΣV^T. Your implementation must return the matrices U, Σ (as a vector of singular values), and V^T. Ensure that U and V are orthogonal matrices and singular values are in descending order.