Let $V$ be an $F$-vector space with $\dim(V) = n$ (which is finite) and let $T$ be an element of the homomorphism from $V$ to $V$. Prove that the diagonals of the upper-triangular matrix of $T$ are the eigenvalues of $T$ without the use of determinants.
Eigenvalues and Upper-triangular Matrices
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linear-algebra
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1Can you assume that an upper triangular matrix with a zero on the diagonal is not invertible? – 2012-11-15
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0What happened to this question ? – 2012-11-15
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4@Philip Please do not vandalize questions. – 2012-11-15