Reduction of a Square Matrix to Triangular Form

Reduction of a Square Matrix to Triangular Form

Given a square matrix A with real or complex entries, there may not exist an invertible matrix S such that S -l AS is diagonal. For instance, cannot be diagonalised in this way (the contrary assumption leads by easy direct calculation, to a contradition); however, this matrix is already upper-triang...

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Veröffentlicht in:Mathematical gazette 1980-12, Vol.64 (430), p.266-270
1. Verfasser: Gerrish, F.
Format: Artikel
Sprache:eng
Schlagworte:
Eigenvalues
Eigenvectors
Geometric planes
Matrices
Parallel lines
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Beschreibung
Zusammenfassung:Given a square matrix A with real or complex entries, there may not exist an invertible matrix S such that S -l AS is diagonal. For instance, cannot be diagonalised in this way (the contrary assumption leads by easy direct calculation, to a contradition); however, this matrix is already upper-triangular.
ISSN:0025-5572
2056-6328
DOI:10.2307/3616727