Math 2.0

Linear and multilinear algebra; matrix theory Proposition

Invertibility of a triangular matrix

Builds on Triangular matrixInvertible matrix

Statement

Let AA be an n×nn \times n triangular matrix over a field. Then AA is an invertible matrix if and only if every entry on its main diagonal is nonzero.

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Invertible matrix, concept, no evidence levelInvertible matrixconceptTriangular matrix, concept, no evidence levelTriangular matrixconceptInvertibility of a triangular matrix, statement, no evidence levelInvertibility of a tr…statement
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  1. Invertible matrix concept
  2. Triangular matrix concept
  3. Invertibility of a triangular matrix statement

Further reading

  1. Web https://github.com/davidaustinm/ula/blob/b6ea263ef23703072b7007485bb7a2d89c5f399b/src/section3-1.xml#L973, src/section3-1.xml:973
About this page
Tag7X1B65CTG4
URIm2://7X1B65CTG4
Kindstatement, proposition
WritingW0 stub
MSC15A09, 15B99
StatusThis copy of the site has no build data. Run m2 status 7X1B65CTG4.
UsesTriangular matrix, Invertible matrix
Changed4 November 2026

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