Re: Re: schur decomposition and mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg66985] Re: [mg66951] Re: schur decomposition and mathematica
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Tue, 6 Jun 2006 06:27:30 -0400 (EDT)
• References: <e5tqf3\$cvk\$1@smc.vnet.net> <200606050747.DAA16299@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On Jun 5, 2006, at 3:47 AM, bghiggins at ucdavis.edu wrote:

> Jeremy,
>
> That is correct. If the eigenvalues are complex, they "appear" in 2X2
> blocks along the diagonal of T in the decomposition A=Q.T.Q* .

If all the elements are real or integer valued.  The following:

SchurDecomposition[{{-5.0 + 0.0 I, 7.0, 6.0, -3.0}, {2.0, -8.0, 3.0,
9.0}, {7.0,
1.0, 2.0, -7.0}, {3.0, 4.0, 4.0, 4.0}}]

returns a triangular decomposition, if you'd rather save yourself the
work of searching for and computing the eigenvalues of 2x2 blocks.

> Jeremy Watts wrote:
>> why upon entering :-
>>
>> SchurDecomposition[{{-5.0, 7.0, 6.0, -3.0}, {2.0, -8.0, 3.0, 9.0},
>> {7.0,
>> 1.0, 2.0, -7.0}, {3.0, 4.0, 4.0, 4.0}}]
>> does mathematica return a 'T matrix' that is not upper triangular?
>>
>> some the eigenvalues are complex, so is it because these
>> eigenvalues reside
>> along the diagonal of 'T' in 2x2 blocks?
>

Regards,

Ssezi

```

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