Triangular matrix: Difference between revisions

Revision as of 14:11, 30 June 2005

Revision as of 14:17, 30 June 2005

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The product of two upper triangular matrices is upper triangular, so the set of upper triangular matrices forms an [[associative algebra|algebra]]. Algebras of upper triangular matrices have a natural generalization in [[functional analysis]] which yields [[nest algebra]]s on [[Hilbert space]]s.

The set of invertible triangular matrices form a [[group (mathematics)|group]]., Itand is a subgroup of all invertible matrices,. andThe isset anof example2 ofby a2 triangular matrices is called the [[parabolicfractional subgrouplinear transformation|parabolic subgroup]]; or3 by 3 and larger normed triangular matrices form the [[Heisenberg group]]. Both are examples of a [[Borel subgroup]].

== Examples ==