Transcription of A Singularly Valuable Decomposition: The SVD of a Matrix
{{id}} {{{paragraph}}}
Example: barber
A Singularly Valuable Decomposition: The SVD of a Matrix
A Singularly Valuable decomposition : The SVD of a MatrixDan KalmanThe American UniversityWashington, DC 20016 February 13, 2002 Every teacher of linear algebra should be familiar with the matrixsingular value decomposition (orSVD). It has interesting and attractive algebraic properties, and conveys important geometrical andtheoretical insights about linear transformations. The close connection between the SVD and the wellknown theory of diagonalization for symmetric matrices makes the topic immediately accessible to linearalgebra teachers, and indeed, a natural extension of what these teachers already know.
uniqueness result for the singular value decomposition. In any SVD of A, the right singular vectors (columns of V) must be the eigenvectors of ATA, the left singular vectors (columns of U) must be the eigenvectors of AAT, and the singular values must be the square roots of the nonzero eigenvalues common to these two symmetric matrices.
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: