Question

singular value decomposition

Answer 1

In linear algebra , the singular-value decomposition (SVD ) is a factorization of a
real or complex matrix. It is the generalization of the eigendecomposition of a positive semidefinite normal matrix (for example, a symmetric matrix with positive eigenvalues) to any matrix via an extension of the polar decomposition. It has many useful applications in signal processing and statistics .
Formally, the singular-value decomposition of an real or complex matrix is a factorization of the form , where is an real or complex unitary matrix ,
is a rectangular diagonal matrix with non-negative real numbers on the diagonal, and is an real or complex unitary matrix. The diagonal entries of are known as the singular values of . The columns of and the columns of are called the left-singular vectors and right-singular vectors of , respectively.