orthonormalization : it seems easy ... but.....
- To: mathgroup at smc.vnet.net
- Subject: [mg16459] orthonormalization : it seems easy ... but.....
- From: "alessandro agresti" <agresti at dffs.unifi.it>
- Date: Sat, 13 Mar 1999 02:21:58 -0500
- Sender: owner-wri-mathgroup at wolfram.com
I am not able to orthonormalize the vectors, see enclosed file please. it seems to me easy but really it is not so. I gave the following cmds: vecs=<<huncvet.asc; <<LinearAlgebra`Orthogonalization` vectorsN=GramSchmidt[vecs] mathematica never ends!!! Thank You very much for Your BIG help... alessandro agresti -------------------------- Alessandro Agresti Universita' degli Studi di Firenze Dipartimento di Fisica, sezione di Fisica Superiore via Santa Marta, 3 50139 Firenze ITALIA tel: 0039 055 4796410 fax: 0039 055 483750 e_mail : agresti at dffs.unifi.it WebPage : http://biz-a.dffs.unifi.it/~agresti/ {{Tan[theta/2]^4/E^(4*I*phi), -(Tan[theta/2]^3/E^(3*I*phi)), -((Sqrt[3]*Tan[theta/2]^3)/E^(3*I*phi)), (Sqrt[3]*Tan[theta/2]^2)/E^(2*I*phi), (Sqrt[3]*Tan[theta/2]^2)/E^(2*I*phi), -((Sqrt[3]*Tan[theta/2])/E^(I*phi)), ((-1 + Cos[theta])*Csc[theta])/E^(I*phi), 1}, {Cot[theta/2]^4/E^(4*I*phi), Cot[theta/2]^3/E^(3*I*phi), (Sqrt[3]*Cot[theta/2]^3)/E^(3*I*phi), (Sqrt[3]*Cot[theta/2]^2)/E^(2*I*phi), (Sqrt[3]*Cot[theta/2]^2)/E^(2*I*phi), (Sqrt[3]*Cot[theta/2])/E^(I*phi), Cot[theta/2]/E^(I*phi), 1}, {E^(-4*I*phi), -(((2*a + Sqrt[4*a^2 + g^2] + g*Cos[theta])*Csc[theta])/(E^(3*I*phi)*g)), ((2*a + Sqrt[4*a^2 + g^2] - 3*g*Cos[theta])*Csc[theta])/ (Sqrt[3]*E^(3*I*phi)*g), ((g + 4*(2*a + Sqrt[4*a^2 + g^2])*Cos[theta] + 3*g*Cos[2*theta])* Csc[theta]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), ((g - 4*(2*a + Sqrt[4*a^2 + g^2])*Cos[theta] + 3*g*Cos[2*theta])* Csc[theta]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), ((2*a + Sqrt[4*a^2 + g^2] + 3*g*Cos[theta])*Csc[theta])/ (Sqrt[3]*E^(I*phi)*g), ((-2*a - Sqrt[4*a^2 + g^2] + g*Cos[theta])* Csc[theta])/(E^(I*phi)*g), 1}, {E^(-4*I*phi), ((-2*a + Sqrt[4*a^2 + g^2] - g*Cos[theta])*Csc[theta])/ (E^(3*I*phi)*g), -(((-2*a + Sqrt[4*a^2 + g^2] + 3*g*Cos[theta])* Csc[theta])/(Sqrt[3]*E^(3*I*phi)*g)), ((g - 4*(-2*a + Sqrt[4*a^2 + g^2])*Cos[theta] + 3*g*Cos[2*theta])* Csc[theta]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), ((g + 4*(-2*a + Sqrt[4*a^2 + g^2])*Cos[theta] + 3*g*Cos[2*theta])* Csc[theta]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), ((2*a - Sqrt[4*a^2 + g^2] + 3*g*Cos[theta])*Csc[theta])/ (Sqrt[3]*E^(I*phi)*g), ((-2*a + Sqrt[4*a^2 + g^2] + g*Cos[theta])* Csc[theta])/(E^(I*phi)*g), 1}, {-(Tan[theta/2]^2/E^(4*I*phi)), ((2*a + Sqrt[4*a^2 - 2*a*g + g^2] + g*Cos[theta])*Sec[theta/2]^2* Tan[theta/2])/(2*E^(3*I*phi)*g), ((-2*a + 2*g - Sqrt[4*a^2 - 2*a*g + g^2] + 3*g*Cos[theta])* Sec[theta/2]^2*Tan[theta/2])/(2*Sqrt[3]*E^(3*I*phi)*g), -((4*a - g + 2*Sqrt[4*a^2 - 2*a*g + g^2] + 3*g*Cos[theta])* Sec[theta/2]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), -((-4*a + g - 2*Sqrt[4*a^2 - 2*a*g + g^2] + 3*g*Cos[theta])* Sec[theta/2]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), ((2*a - 2*g + Sqrt[4*a^2 - 2*a*g + g^2] + 3*g*Cos[theta])*Csc[theta])/ (Sqrt[3]*E^(I*phi)*g), ((-2*a - Sqrt[4*a^2 - 2*a*g + g^2] + g*Cos[theta])*Csc[theta])/(E^(I*phi)*g), 1}, {-(Tan[theta/2]^2/E^(4*I*phi)), ((2*a - Sqrt[4*a^2 - 2*a*g + g^2] + g*Cos[theta])*Sec[theta/2]^2* Tan[theta/2])/(2*E^(3*I*phi)*g), ((-2*a + 2*g + Sqrt[4*a^2 - 2*a*g + g^2] + 3*g*Cos[theta])* Sec[theta/2]^2*Tan[theta/2])/(2*Sqrt[3]*E^(3*I*phi)*g), ((-4*a + g + 2*Sqrt[4*a^2 - 2*a*g + g^2] - 3*g*Cos[theta])* Sec[theta/2]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), -((-4*a + g + 2*Sqrt[4*a^2 - 2*a*g + g^2] + 3*g*Cos[theta])* Sec[theta/2]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), ((2*a - 2*g - Sqrt[4*a^2 - 2*a*g + g^2] + 3*g*Cos[theta])*Csc[theta])/ (Sqrt[3]*E^(I*phi)*g), ((-2*a + Sqrt[4*a^2 - 2*a*g + g^2] + g*Cos[theta])*Csc[theta])/(E^(I*phi)*g), 1}, {-(Cot[theta/2]^2/E^(4*I*phi)), ((2*a + Sqrt[4*a^2 + 2*a*g + g^2] + g*Cos[theta])*Cot[theta/2]* Csc[theta/2]^2)/(2*E^(3*I*phi)*g), -((2*a + 2*g + Sqrt[4*a^2 + 2*a*g + g^2] - 3*g*Cos[theta])*Cot[theta/2]* Csc[theta/2]^2)/(2*Sqrt[3]*E^(3*I*phi)*g), ((4*a + g + 2*Sqrt[4*a^2 + 2*a*g + g^2] + 3*g*Cos[theta])* Csc[theta/2]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), -((4*a + g + 2*Sqrt[4*a^2 + 2*a*g + g^2] - 3*g*Cos[theta])* Csc[theta/2]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), ((2*a + 2*g + Sqrt[4*a^2 + 2*a*g + g^2] + 3*g*Cos[theta])*Csc[theta])/ (Sqrt[3]*E^(I*phi)*g), ((-2*a - Sqrt[4*a^2 + 2*a*g + g^2] + g*Cos[theta])*Csc[theta])/(E^(I*phi)*g), 1}, {-(Cot[theta/2]^2/E^(4*I*phi)), ((2*a - Sqrt[4*a^2 + 2*a*g + g^2] + g*Cos[theta])*Cot[theta/2]* Csc[theta/2]^2)/(2*E^(3*I*phi)*g), ((-2*a - 2*g + Sqrt[4*a^2 + 2*a*g + g^2] + 3*g*Cos[theta])*Cot[theta/2]* Csc[theta/2]^2)/(2*Sqrt[3]*E^(3*I*phi)*g), ((4*a + g - 2*Sqrt[4*a^2 + 2*a*g + g^2] + 3*g*Cos[theta])*Csc[theta/2]^2)/ (2*Sqrt[3]*E^(2*I*phi)*g), -((4*a + g - 2*Sqrt[4*a^2 + 2*a*g + g^2] - 3*g*Cos[theta])*Csc[theta/2]^2)/(2*Sqrt[3]*E^(2*I*phi)*g), ((2*a + 2*g - Sqrt[4*a^2 + 2*a*g + g^2] + 3*g*Cos[theta])*Csc[theta])/ (Sqrt[3]*E^(I*phi)*g), ((-2*a + Sqrt[4*a^2 + 2*a*g + g^2] + g*Cos[theta])*Csc[theta])/(E^(I*phi)*g), 1}}