SVD is a factorization of a real or complex matrix. 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 .
is an real or complex unitary matrix.
is an rectangular diagnal matrix with non-negative real numbers on the diagnal.
is an real or complex unitary matrix.
the diagnal entries of are known as the singular values of .
the left-singular vectors: columns of matrix .
the right-singular vectors: columns of matrix .
Wikipedia https://en.wikipedia.org/wiki/Singular_value_decomposition
unitary matrix : a complex square matrix is unitary if its conjugate transpose is also its inverse — that is, if
where is the identity matrix.
is the conjugate transpose of matrix .
identity matrix: is the square matrix with ones on the main diagnal and zeros else where.
the left-singular vectors of are a set of orthonormal eigenvectors of :