Singular Value Decomposition

Singular Value Decomposition (SVD) is a mathematical technique that breaks down a complex matrix into simpler, easier-to-analyze parts. Think of it like decomposing a complex object into its basic building blocks—directions and scales—highlighting the most important patterns or features. SVD expresses the original data as a product of three matrices: one capturing the main directions (singular vectors), one with scaling factors (singular values), and another representing the original space. This process helps in data compression, noise reduction, and understanding the structure of large datasets across various fields.