**Example**

Consider the 4×5 matrix

A singular value decomposition of this matrix is given by

Notice is zero outside of the diagonal and one diagonal element is zero. Furthermore, because the matrices and are unitary, multiplying by their respective conjugate transposes yields identity matrices, as shown below. In this case, because and are real valued, they each are an orthogonal matrix.

and

This particular singular value decomposition is not unique. Choosing such that

is also a valid singular value decomposition.

Read more about this topic: Singular Value Decomposition

### Other articles related to "example":

**Example**

**Example** may also refer to:

- Example (musician), a British musician
*Example*, Florida rock band For Squirrels' sole major-label album, released in 1995- example.com, example.net, example.org, example.edu and .example, domain names reserved for use in documentation as examples
- HMS
*Example*(P165), an Archer-class patrol and training vessel of the British Royal Navy *The Example*, a 1634 play by James Shirley*The Example*(comics), a 2009 graphic novel by Tom Taylor and Colin Wilson

**Example**

4 ... Next we have to scale the structures up by increasing m ...

**Example**

... Then the projection on the first component of a distribution's wave front set is nothing else than its classical singular support, i.e ... the complement of the set on which its restriction would be a smooth function ...

### Famous quotes containing the word example:

“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, *example* by *example*, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”

—Marcel Proust (1871–1922)