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

**References**:**Re: schur decomposition and mathematica***From:*bghiggins@ucdavis.edu