Diagonalization of square matrix if not all eigenvalues are distinct of

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A square matrix can be diagonalized even if not all eigenvalues are distinct. To achieve this, one must identify the eigenspaces and establish a basis for them. If the basis vectors from the eigenspaces span the entire space, the matrix is diagonalizable. The diagonal matrix can be constructed using these basis eigenvectors. Therefore, diagonalization is feasible under these conditions.
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Is it possible to diagonalize such matrix? and how would one do it?
 
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Yes, it is possible to diagonalize such a matrix. One has to find the eigenspaces and a basis for the eigenspaces. Take all the basisvectors for the eigenspaces, if they span the entire space, then the matrix is diagonalizable.
Taking all the basis eigenvectors as a basis gives you the required diagonal matrix.
 

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