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Subject: Finding the nearest matrix with real eigenvalues From: Gary B Date: 31 Aug, 2010 15:14:07 Message: 1 of 22 
Hi, 
Subject: Finding the nearest matrix with real eigenvalues From: John D'Errico Date: 31 Aug, 2010 16:00:11 Message: 2 of 22 
"Gary B" <bargaryg@tcd.ie> wrote in message <i5j67v$4s4$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Roger Stafford Date: 31 Aug, 2010 18:41:19 Message: 3 of 22 
"Gary B" <bargaryg@tcd.ie> wrote in message <i5j67v$4s4$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Bruno Luong Date: 31 Aug, 2010 20:04:04 Message: 4 of 22 
"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <i5jicf$29u$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Roger Stafford Date: 31 Aug, 2010 22:22:05 Message: 5 of 22 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <i5jn7k$pdd$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Roger Stafford Date: 1 Sep, 2010 14:12:20 Message: 6 of 22 
"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <i5jvad$c2b$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: John D'Errico Date: 1 Sep, 2010 14:26:22 Message: 7 of 22 
"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <i5ln03$lje$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Bruno Luong Date: 1 Sep, 2010 15:36:21 Message: 8 of 22 
John and Roger, 
Subject: Finding the nearest matrix with real eigenvalues From: Gary B Date: 2 Sep, 2010 19:09:18 Message: 9 of 22 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <i5lrtl$ip8$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Matt J Date: 2 Sep, 2010 20:47:20 Message: 10 of 22 

Subject: Finding the nearest matrix with real eigenvalues From: Matt J Date: 2 Sep, 2010 21:37:20 Message: 11 of 22 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <i5p2gn$o5$1@fred.mate hworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Matt J Date: 2 Sep, 2010 22:02:20 Message: 12 of 22 
"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <i5jvad$c2b$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Bruno Luong Date: 2 Sep, 2010 22:36:07 Message: 13 of 22 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <i5p6tb$f0b$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Roger Stafford Date: 2 Sep, 2010 23:45:23 Message: 14 of 22 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <i5p2gn$o5t$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Bruno Luong Date: 3 Sep, 2010 06:35:26 Message: 15 of 22 
"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <i5pcuj$9en$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Matt J Date: 3 Sep, 2010 10:01:22 Message: 16 of 22 
"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <i5pcuj$9en$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Matt J Date: 3 Sep, 2010 10:18:08 Message: 17 of 22 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <i5p8sn$mid$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Bruno Luong Date: 3 Sep, 2010 11:12:07 Message: 18 of 22 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <i5qi10$6oo$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Matt J Date: 3 Sep, 2010 14:29:09 Message: 19 of 22 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <i5ql67$sp0$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Matt J Date: 3 Sep, 2010 14:50:24 Message: 20 of 22 
In any case, I can now confirm that Roger's solution minimizes neither the Frobenius norm nor the spectral norm. The following gives a counterexample 
Subject: Finding the nearest matrix with real eigenvalues From: Bruno Luong Date: 3 Sep, 2010 17:31:21 Message: 21 of 22 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <i5r1vg$mg5$1@fred.mathworks.com>... 
Subject: Finding the nearest matrix with real eigenvalues From: Roger Stafford Date: 3 Sep, 2010 22:01:09 Message: 22 of 22 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <i5r1vg$mg5$1@fred.mathworks.com>... 
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