Editing Matrix decomposition (section)

=== Singular value decomposition ===
{{main|Singular value decomposition}}
*Applicable to: ''m''-by-''n'' matrix ''A''.
*Decomposition: <math>A=UDV^*</math>, where ''D'' is a nonnegative [[diagonal matrix]], and ''U'' and ''V'' satisfy <math>U^*U = I, V^*V = I</math>. Here <math>V^*</math> is the [[conjugate transpose]] of ''V'' (or simply the [[matrix transpose|transpose]], if ''V'' contains real numbers only), and ''I'' denotes the identity matrix (of some dimension). 
*Comment: The diagonal elements of ''D'' are called the [[singular value]]s of ''A''.
*Comment: Like the eigendecomposition above, the singular value decomposition involves finding basis directions along which matrix multiplication is equivalent to scalar multiplication, but it has greater generality since the matrix under consideration need not be square.
*Uniqueness: the singular values of <math>A</math> are always uniquely determined. <math>U</math> and <math>V</math> need not to be unique in general.