How To Perform Singular Value Decomposition (SVD) On A Matrix
SVD decomposes matrices into U, Σ, and V^T components, simplifying complex data for analysis and insights.
Singular Value Decomposition (SVD) is a key concept in matrices, particularly useful in machine learning, data compression, and dimensionality reduction. It allows us to express a matrix in a way that reveals its underlying structure and properties.
What is SVD?
For any ( m times n ) matrix ( A ), SVD breaks it down into three matrices:
A = U Σ V^T
Where:
( U ) is an ( m times m ) orthogonal matrix whose columns are the left singular vectors.
( Σ ) is an ( m times n ) diagonal matrix containing the singular values.
( V ) is an ( n times n ) orthogonal matr...