Search results
Results from the WOW.Com Content Network
Specifically, the singular value decomposition of an complex matrix is a factorization of the form =, where is an complex unitary matrix, is an rectangular diagonal matrix with non-negative real numbers on the diagonal, is an complex unitary matrix, and is the conjugate transpose of . Such decomposition ...
Singular value - Wikipedia
[14] [5] [17] If = is the singular value decomposition of , then + = +. For a rectangular diagonal matrix such as Σ {\displaystyle \Sigma } , we get the pseudoinverse by taking the reciprocal of each non-zero element on the diagonal, leaving the zeros in place.
The generalized singular value decomposition (GSVD) is a matrix decomposition on a pair of matrices which generalizes the singular value decomposition.It was introduced by Van Loan [1] in 1976 and later developed by Paige and Saunders, [2] which is the version described here.
In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded as one type of generalization of the matrix singular value decomposition. It has applications in computer vision, computer graphics, machine learning, scientific computing, and signal ...
In linear algebra, two-dimensional singular-value decomposition (2DSVD) computes the low-rank approximation of a set of matrices such as 2D images or weather maps in a manner almost identical to SVD (singular-value decomposition) which computes the low-rank approximation of a single matrix (or a set of 1D vectors). SVD
The singular value decomposition of a matrix is = where U and V are unitary, and is diagonal.The diagonal entries of are called the singular values of A.Because singular values are the square roots of the eigenvalues of , there is a tight connection between the singular value decomposition and eigenvalue decompositions.
The singular value decomposition of the Hankel matrix provides a means of computing the A, B, and C matrices which define the state-space realization. [4] The Hankel matrix formed from the signal has been found useful for decomposition of non-stationary signals and time-frequency representation.