Prove that all normal matrices are semi-simple using Schur's decomposition
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Is there any elegant proof that shows that all normal matrices are semi-simple that comes from Schur's decomposition or its corrolaries? There is a proof that normal matrices are unitary diagonizable and then that diagonizable matrices are semi-simple, but it seems a little exhaustive to combine them both. Is there any better proof?
proof-writing diagonalization matrix-decomposition
asked Dec 17 '18 at 15:33
ViniLLViniLL
247
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add a comment |
$begingroup$
Is there any elegant proof that shows that all normal matrices are semi-simple that comes from Schur's decomposition or its corrolaries? There is a proof that normal matrices are unitary diagonizable and then that diagonizable matrices are semi-simple, but it seems a little exhaustive to combine them both. Is there any better proof?
proof-writing diagonalization matrix-decomposition
asked Dec 17 '18 at 15:33
ViniLLViniLL
247
$endgroup$
add a comment |
$begingroup$
Is there any elegant proof that shows that all normal matrices are semi-simple that comes from Schur's decomposition or its corrolaries? There is a proof that normal matrices are unitary diagonizable and then that diagonizable matrices are semi-simple, but it seems a little exhaustive to combine them both. Is there any better proof?
proof-writing diagonalization matrix-decomposition
asked Dec 17 '18 at 15:33
ViniLLViniLL
247
$endgroup$
Is there any elegant proof that shows that all normal matrices are semi-simple that comes from Schur's decomposition or its corrolaries? There is a proof that normal matrices are unitary diagonizable and then that diagonizable matrices are semi-simple, but it seems a little exhaustive to combine them both. Is there any better proof?
proof-writing diagonalization matrix-decomposition
proof-writing diagonalization matrix-decomposition
asked Dec 17 '18 at 15:33
ViniLLViniLL
247
asked Dec 17 '18 at 15:33
ViniLLViniLL
247
asked Dec 17 '18 at 15:33
ViniLLViniLL
247
asked Dec 17 '18 at 15:33
ViniLLViniLL
247
asked Dec 17 '18 at 15:33
ViniLLViniLL
247
247
add a comment |
add a comment |
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