Relationship between the diagonalizable matrix and diagonal matrix

label Mathematics
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Show that if A is diagonalizable, then A must be diagonal

Apr 22nd, 2015
Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental properties of the underlying matrix. Matrix diagonalization is equivalent to transforming the underlying system of equations into a special set of coordinate axes in which the matrix takes this canonical form. Diagonalizing a matrix is also equivalent to finding the matrix's eigenvalues, which turn out to be precisely the entries of the diagonalized matrix. Similarly, the eigenvectors make up the new set of axes corresponding to the diagonal matrix.


Apr 22nd, 2015

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Apr 22nd, 2015
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