Is it possible for a diagonalisable and non-zero n x n matrix A to have a diagonal matrix D with all zero diagonal entries?
2026-04-02 11:44:19.1775130259
Diagonal matrix with all zero entries
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If $A$ is diagonalizable and all its eigenvalues are zero, then $A=0$. Because there is a basis of eigenvectors $f_1,\ldots,f_n$, and all satisfy $Af_j=0$; so $A=0$.