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Singular Value Decomposition (SVD) is one of the most powerful and versatile tools in linear algebra. It breaks down any matrix—even a non-square one—into three simpler matrices that reveal its fundamental structure: one that captures its directions (U), one that scales them (Σ), and one that rotates or reflects them (Vᵀ). At its core, SVD helps us understand how a matrix transforms space by identifying the principal components of that transformation. SVD is everywhere—from data science and mach