Editing Vandermonde matrix (section)

===Rank of the Vandermonde matrix===

* An {{math|''m'' × ''n''}} rectangular Vandermonde matrix such that {{math|''m'' ≤ ''n''}} has [[rank of a matrix|rank]] {{math|''m''}} [[if and only if]] all {{math|''x''<sub>''i''</sub>}} are distinct.
* An {{math|''m'' × ''n''}} rectangular Vandermonde matrix such that {{math|''m'' ≥ ''n''}} has [[rank of a matrix|rank]] {{math|''n''}} if and only if there are {{mvar|n}} of the {{math|''x''<sub>''i''</sub>}} that are distinct.
* A square Vandermonde matrix is [[invertible matrix|invertible]] if and only if the {{math|''x''<sub>''i''</sub>}} are distinct. An explicit formula for the inverse is known (see below).<ref>{{Cite book
| title = Inverse of the Vandermonde matrix with applications
| last = Turner
| first = L. Richard
| date = August 1966
| url =https://ntrs.nasa.gov/api/citations/19660023042/downloads/19660023042.pdf
}}</ref><ref name="MS">{{Cite journal
| volume = 65
| issue = 2
| pages = 95–100
| last = Macon
| first = N.
|author2=A. Spitzbart
 | title = Inverses of Vandermonde Matrices
| journal = The American Mathematical Monthly
| date = February 1958
| jstor = 2308881
| doi = 10.2307/2308881}}</ref>