= Defective matrix
{title2=$\dim E_\lambda<m_{\mathrm{alg}}(\lambda)$}
A <matrix> is defective when an <eigenvalue> has <geometric multiplicity> smaller than its <algebraic multiplicity>. Over a <field> in which the <characteristic polynomial> splits, this is precisely the obstruction to an <eigenbasis>: at least one <Jordan block> has size greater than one, and <generalized eigenvectors> are needed to complete a <basis>. The <shear mapping> in <diagonalizable matrix> is the simplest example.
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