Matrix diagonalisation computations

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JamesGoh
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For matrix diagonalisation, is it necessary to compute the P and D matrix ?

Once you have the eigenvectors, isn't it just simply a case of putting them into the P matrix

Likewise, with the eigenvalues, don't you just put them along the diagonal axis of D to form D ?
 
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Yes, to both of your last statements. But isn't that exactly what "compute the P and D matrix" means? You "compute the P and D matrices" by finding the eigenvalues and corresponding eigenvectors of the original matrix.