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Example 1.
Find the Jacobson radical of the set of matrices M.
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| (2.1) |
| (2.2) |
Clearly each one of these matrices is nilpotent. Note that J = [M[2], M[4], M[5]]. We check that J is also the nilradical of M, when viewed as an abstract Lie algebra.
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| (2.3) |