About: Diagonalization of a matrix

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Diagonalization is the process of finding a corresponding diagonal matrix (a matrix in which the only non-zero components are on the diagonal line from to for an matrix) for a given diagonalizable matrix. A matrix is diagonalizable if and only if the matrix of eigenvectors is invertable (that is, the determinant does not equal zero). If a matrix is not diagonalizable, is is called a defective matrix.

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rdfs:label	Diagonalization of a matrix
rdfs:comment	Diagonalization is the process of finding a corresponding diagonal matrix (a matrix in which the only non-zero components are on the diagonal line from to for an matrix) for a given diagonalizable matrix. A matrix is diagonalizable if and only if the matrix of eigenvectors is invertable (that is, the determinant does not equal zero). If a matrix is not diagonalizable, is is called a defective matrix.
dcterms:subject	Linear algebra
abstract	Diagonalization is the process of finding a corresponding diagonal matrix (a matrix in which the only non-zero components are on the diagonal line from to for an matrix) for a given diagonalizable matrix. A matrix is diagonalizable if and only if the matrix of eigenvectors is invertable (that is, the determinant does not equal zero). If a matrix is not diagonalizable, is is called a defective matrix. The diagonal of a matrix is equal to such that is the matrix of eigenvectors (). Diagonal matrices are very useful, as computing determinants, products and sums of matrices, and powers becomes much simpler. For example, given the matrix , .

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