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Channel: Is this matrix diagonalizable over $\mathbb{R}$ or $\mathbb{C}$? - Mathematics Stack Exchange
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Answer by Chiranjeev_Kumar for Is this matrix diagonalizable over...

Nothing to calculate: Note that Given matrix is Lower triangular, hence Diagonal entries of matrix are eigenvalues. So, eigenvalues are $2,6$ which are distinct and real , Hence matrix is...

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Answer by Ben Grossmann for Is this matrix diagonalizable over $\mathbb{R}$...

You miscalculated the determinant. You should have ended up with the characteristic polynomial $$p(x) = (x-6)(x-2)$$check your work, note that $0 \times (-2) = 0$.

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Is this matrix diagonalizable over $\mathbb{R}$ or $\mathbb{C}$?

Problem: Let $A = \begin{pmatrix} 6 & 0 \\ -2 & 2 \end{pmatrix}$. Is this matrix diagonalizable over $\mathbb{R}$? If not, is it diagonalizable over $\mathbb{C}$? Compute the eigenvalues...

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