SVD Calculator

Calculates the singular value decomposition (SVD) for input matrices, breaking down a complex matrix into three simpler components. The process decomposes an original matrix A into the product of three other matrices: U, Σ, and V transpose. Specifically, it determines the orthogonal matrix U containing left singular vectors, the diagonal matrix Σ holding the singular values, and the orthogonal matrix V containing right singular vectors. Users input a numerical matrix, and the tool outputs these constituent parts, demonstrating the fundamental mathematical relationship A = UΣV^T. Students of linear algebra, data scientists, and machine learning practitioners utilize this calculator to understand core concepts in dimensionality reduction and principal component analysis.