Singular Value Decomposition

Synonyms

Latent semantic indexing; Principle component analysis; SVD transformation

Definition

The SVD definition of a matrix is illustrated as follows [1]: For a real matrix A = [a _ij ] _m × n , without loss of generality, suppose m ≥ n and there exists SVD of A (shown in Fig. 1):

$$ A=U\left(\begin{array}{l}{\Sigma}_1\\ {}0\end{array}\right){V}^T={U}_{m\times m}{\sum}_{m\times n}{V}_{n\times n}^T $$

Fig. 1

SVD transformation of matrix and its approximation