Let V be an n-dimensional vector space over the field F and let T be a linear operator on V such that the range and null space of T are identical. Prove that n is even. Give an example of such linear operator.
2026-03-25 17:19:51.1774459191
Let V be an n-dimensional vector space over the field F and let T be a linear operator on V
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Rank-Nulity theorem says that the dimension of the kernel + dimension of the image equals n.
An example:
$\begin {bmatrix} 1&1\\-1&-1 \end{bmatrix}$