About: EP matrix

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

In mathematics, an EP matrix (or range-Hermitian matrix or RPN matrix) is a square matrix A whose range is equal to the range of its conjugate transpose A*. Another equivalent characterization of EP matrices is that the range of A is orthogonal to the nullspace of A. Thus, EP matrices are also known as RPN (Range Perpendicular to Nullspace) matrices. The range of any matrix A is perpendicular to the null-space of A*, but is not necessarily perpendicular to the null-space of A. When A is an EP matrix, the range of A is precisely perpendicular to the null-space of A.

Property Value
dbo:abstract
  • In mathematics, an EP matrix (or range-Hermitian matrix or RPN matrix) is a square matrix A whose range is equal to the range of its conjugate transpose A*. Another equivalent characterization of EP matrices is that the range of A is orthogonal to the nullspace of A. Thus, EP matrices are also known as RPN (Range Perpendicular to Nullspace) matrices. EP matrices were introduced in 1950 by Hans Schwerdtfeger, and since then, many equivalent characterizations of EP matrices have been investigated through the literature. The meaning of the EP abbreviation stands originally for Equal Principal, but it is widely believed that it stands for Equal Projectors instead, since an equivalent characterization of EP matrices is based in terms of equality of the projectors AA+ and A+A. The range of any matrix A is perpendicular to the null-space of A*, but is not necessarily perpendicular to the null-space of A. When A is an EP matrix, the range of A is precisely perpendicular to the null-space of A. (en)
dbo:wikiPageID
  • 59859530 (xsd:integer)
dbo:wikiPageLength
  • 4261 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1015297528 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
rdfs:comment
  • In mathematics, an EP matrix (or range-Hermitian matrix or RPN matrix) is a square matrix A whose range is equal to the range of its conjugate transpose A*. Another equivalent characterization of EP matrices is that the range of A is orthogonal to the nullspace of A. Thus, EP matrices are also known as RPN (Range Perpendicular to Nullspace) matrices. The range of any matrix A is perpendicular to the null-space of A*, but is not necessarily perpendicular to the null-space of A. When A is an EP matrix, the range of A is precisely perpendicular to the null-space of A. (en)
rdfs:label
  • EP matrix (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageRedirects of
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License