F. Gerrish
Abstract
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.
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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.
Key concepts: Square matrix, Invertible matrix, Triangular matrix, Square (algebra), Mathematics, Diagonal, Matrix (chemical analysis), Reduction (mathematics)