orthonormal vectors: I need help, please........
- To: mathgroup at smc.vnet.net
- Subject: [mg16636] orthonormal vectors: I need help, please........
- From: "alessandro agresti" <agresti at dffs.unifi.it>
- Date: Fri, 19 Mar 1999 12:53:55 -0500
- Sender: owner-wri-mathgroup at wolfram.com
{{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}}
I have eight vectors , see please above. These vectors are
neither orthogonal nor normalized.
I would like to have these vectors orthonormalized.
I think that the right procedure is LinearAlgebra`Orthogonalization`
GramSchmidt , but I am not able to use it.
Can anybody help me ?
Again, thank You for Your BIG help
alessandro
--------------------------
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/