Re: Re: Mathematica 7 is now available

• To: mathgroup at smc.vnet.net
• Subject: [mg93719] Re: [mg93711] Re: Mathematica 7 is now available
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 24 Nov 2008 04:11:45 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <gg0qf8\$c6\$1@smc.vnet.net> <gg3c6m\$k2t\$1@smc.vnet.net> <200811221114.GAA20643@smc.vnet.net>

```Mathematica 7.0 (Windows 32 bit).  For your mat:

N@Eigenvalues[mat] // InputForm

{-9.091215416949623, -7.4185507188738455, -7.4185507188738455,
-7.291502622129181, 4.337337307188519, -4., -4., 3.2915026221291814,
-3.2461218902388955, -2.387873132949261, -2.387873132949261,
1.8064238518231066, 1.8064238518231066, 0.}

Szabolcs wrote:
> On Nov 21, 11:32 am, Michael Weyrauch <michael.weyra... at gmx.de> wrote:
>> The Tally[] problem is solved. This I checked with a prerelease version
>> of Mathematica 7 I got at this year's Mathematica users conference.
>>
>
> What about the other bug (the eigenvalue problem), linked from the
>
> I copied the (wrong) results from Mathematica 6 here:
>
>
> In[1]:= mat = {{-6, 0, -Sqrt[3], 0, 0, Sqrt[3], 0, 0, 0, 0, 0, 0, 0,
>     0}, {0, -6, 0, -Sqrt[3], 0, 0, Sqrt[3], 0, 0, 0, 0, 0, 0,
>     0}, {-Sqrt[3], 0, -4, 2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4),
>     2 Sqrt[2/3], 0, 0, Sqrt[3], 0, 0, 0, 0, 0, 0}, {0, -Sqrt[3],
>     2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4), -4/3, -(2 Sqrt[2])/3, 0, 0, 0,
>      Sqrt[3], 0, 0, 0, 0, 0}, {0, 0, 2 Sqrt[2/3], -(2 Sqrt[2])/3, 7/3,
>      0, 0, 0, 0, Sqrt[3], 0, 0, 0, 0}, {Sqrt[3], 0, 0, 0, 0, -4, 0,
>     2 (-1/(4 Sqrt[3]) + Sqrt[3]/4), 0, 0, 2 Sqrt[2/3], 0, 0, 0}, {0,
>     Sqrt[3], 0, 0, 0, 0, -4, 0, 2 (-1/(4 Sqrt[3]) + Sqrt[3]/4), 0, 0,
>     2 Sqrt[2/3], 0, 0}, {0, 0, Sqrt[3], 0, 0,
>     2 (-1/(4 Sqrt[3]) + Sqrt[3]/4), 0, -14/3,
>     2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4), 2 Sqrt[2/3], (2 Sqrt[2])/3, 0,
>      0, 0}, {0, 0, 0, Sqrt[3], 0, 0, 2 (-1/(4 Sqrt[3]) + Sqrt[3]/4),
>     2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4), -2, -(2 Sqrt[2])/3,
>     0, (2 Sqrt[2])/3, 0, 0}, {0, 0, 0, 0, Sqrt[3], 0, 0,
>     2 Sqrt[2/3], -(2 Sqrt[2])/3, -7/3, 0, 0,
>     2 (1/(3 Sqrt[2]) + (2 Sqrt[2])/3), Sqrt[10/3]}, {0, 0, 0, 0, 0,
>     2 Sqrt[2/3], 0, (2 Sqrt[2])/3, 0, 0, -16/3,
>     2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4), 2 Sqrt[2/3], 0}, {0, 0, 0, 0,
>     0, 0, 2 Sqrt[2/3], 0, (2 Sqrt[2])/3, 0,
>     2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4), -8/3, -(2 Sqrt[2])/3, 0}, {0,
>     0, 0, 0, 0, 0, 0, 0, 0, 2 (1/(3 Sqrt[2]) + (2 Sqrt[2])/3),
>     2 Sqrt[2/3], -(2 Sqrt[2])/3, 1/2,
>     2 (-Sqrt[5/3]/16 - Sqrt[15]/16)}, {0, 0, 0, 0, 0, 0, 0, 0, 0,
>     Sqrt[10/3], 0, 0, 2 (-Sqrt[5/3]/16 - Sqrt[15]/16), 7/2}};
>
> In[2]:= mat === Conjugate@Transpose[mat]
> Out[2]= True
>
> (mat is Hermitian so we expect real eigenvalues.)
>
> In[3]:= N@Eigenvalues[mat]
>
> Out[3]= {-9.41358 + 0.88758 I, -9.41358 - 0.88758 I, -7.37965 +
>   2.32729 I, -7.37965 - 2.32729 I, -4.46655 + 2.59738 I, -4.46655 -
>   2.59738 I, 4.36971, 3.21081, -2.32456 + 2.10914 I, -2.32456 -
>   2.10914 I, 2.04366+ 0.552265 I,
>  2.04366- 0.552265 I, -0.249588 + 1.29034 I, -0.249588 - 1.29034 I}
>
> In[4]:= Eigenvalues[N[mat]]
>
> Out[4]= {-9.09122, -7.41855, -7.41855, -7.2915, 4.33734, -4., -4., \
> 3.2915, -3.24612, -2.38787, -2.38787, 1.80642, 1.80642,
>  9.21707*10^-16}
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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