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Matrix multiplication T2*T1, I am not getting the output

Kumar Arpit
Posted 5 years ago 
a = \[Alpha]*(r + s)/2 /. {r -> 0.00037, s -> 0.0013};
            b = \[Alpha]*(\[Alpha]*r*s - 1) /. {r -> 0.00037, s -> 0.0013};
            Subscript[\[Beta], 1] = Sqrt[Sqrt[a^2 - b] - a];
            Subscript[\[Beta], 2] = Sqrt[Sqrt[a^2 - b] + a];
            Subscript[m, 
              1] = (\[Alpha]*s + Subscript[\[Beta], 1]^2)/Subscript[\[Beta], 1];
            Subscript[m, 
              2] = (\[Alpha]*s - Subscript[\[Beta], 2]^2)/Subscript[\[Beta], 2];
            T1 = {{1, 0, 1, 0}, {Subscript[m, 1]*Subscript[\[Beta], 1], 0, 
                 Subscript[m, 2]*Subscript[\[Beta], 2], 
                 0}, {0, (Subscript[\[Beta], 1] - Subscript[m, 1]), 
                 0, (Subscript[\[Beta], 2] + Subscript[m, 2])}, {-Subscript[m, 1]*
                  Subscript[\[Beta], 1]*t, Subscript[\[Beta], 
                 1], -Subscript[m, 2]*Subscript[\[Beta], 2]*t, Subscript[\[Beta], 
                 2]}} /. {t -> 0.2154};
            T2 = Inverse[{{Cosh[Subscript[\[Beta], 1]/2], 
                Sinh[Subscript[\[Beta], 1]/2], Cos[Subscript[\[Beta], 2]/2], 
                Sin[Subscript[\[Beta], 2]/2]}, {Subscript[m, 1]*Subscript[\[Beta],
                  1]*Cosh[Subscript[\[Beta], 1]/2], 
                Subscript[m, 1]*Subscript[\[Beta], 1]*
                 Sinh[Subscript[\[Beta], 1]/2], 
                Subscript[m, 2]*Subscript[\[Beta], 2]*
                 Cos[Subscript[\[Beta], 2]/2], 
                Subscript[m, 2]*Subscript[\[Beta], 2]*
                 Sin[Subscript[\[Beta], 2]/2]}, {(Subscript[\[Beta], 1] - 
                   Subscript[m, 1])*
                 Sinh[Subscript[\[Beta], 1]/2], (Subscript[\[Beta], 1] - 
                   Subscript[m, 1])*
                 Cosh[Subscript[\[Beta], 1]/
                   2], -(Subscript[\[Beta], 2] + Subscript[m, 2])*
                 Sin[Subscript[\[Beta], 2]/2], (Subscript[\[Beta], 2] + Subscript[
                   m, 2])*Cos[Subscript[\[Beta], 2]/2]}, {Subscript[\[Beta], 1]*
                 Sinh[Subscript[\[Beta], 1]/2], 
                Subscript[\[Beta], 1]*
                 Cosh[Subscript[\[Beta], 1]/2], -Subscript[\[Beta], 2]*
                 Sin[Subscript[\[Beta], 2]
                   /2], Subscript[\[Beta], 2]*Cos[Subscript[\[Beta], 2]/2]}}]
POSTED BY: Kumar Arpit
3 Replies
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Anonymous User
Anonymous User
Posted 5 years ago

I got the output without difficulty. The dimensions of T1 and T2 are 4x4. T1 has eigenvalues (T2 I didn't wait for), T2 Inverses quickly. The 4x4 multiplication is done rapidly. I cannot post the output.
POSTED BY: Anonymous User
Kumar Arpit
Kumar Arpit
Posted 5 years ago

Would you please give me the screen shot of the output or can you please tell me which of the matrix element are zero after multiplication of Inverse T2 and T1.

POSTED BY: Kumar Arpit
Bill Nelson
Bill Nelson
Posted 5 years ago

This

FullSimplify[Simplify[T2.T1]/.{
  Sqrt[-0.000835*α+Sqrt[α+2.162250000000001*^-7*α^2]]->c1,
  Sqrt[0.000835*α+Sqrt[α+2.162250000000001*^-7*α^2]]->c2,
  Sqrt[α + 2.162250000000001*^-7*α^2]->c3,
  1.5302219679556523*^-17->c4,
  - 1.5302219679556523*^-17->-c4,
  3.308722450212111*^-24->c5,
  -3.308722450212111*^-24->-c5,
  3.0604439359113046*^-17->c6,
  -3.0604439359113046*^-17->-c6}]

returns this

{{((α*(-5.014231344597081*^-13+4.624812117007744*^6*s-1.1954859124653531*^-19*
α+0.9999999999999997*s*α)+c3*(-1.2836432242168526*^-10-2.775557561562891*^-17*
α+2.567286448433705*^-10*s^2*α))*Cosh[c1/2]+c1*(c3*(5.2737569903623595*^-17+s*
(-415.90704127644807+498092.265001734*s))*α+s*(498092.265001734+0.10770000000000003*
α)*α+7.651109839778262*^-18*s*α^2*Cos[c2]+c2*(-5.35921046110536*^-14-
6.418216121084263*^-11*s)*(c3+s*α)*Sin[c2])*Sinh[c1/2])/(α*(1.*c3*c4+
4.6248121170077445*^6*s+1.*s*α+1.*c3*c4*Cos[c2]+c3*c4*(-1.-1.*Cos[c2])*Cosh[c1])),
((1.*c3*c6+s*(4.6248121170077445*^6+1.*α)+1.*c3*c6*Cos[c2])*Sinh[c1/2])/(-1.*
c3*c4-4.6248121170077445*^6*s-1.*s*α-1.*c3*c4*Cos[c2]+c3*c4*(1.+1.*Cos[c2])*Cosh[c1]),
((α*(-2.1436841844421449*^-13-1.2836432242168526*^-10*s-4.6351811278100287*^-20*α-
1.1725439031608844*^-16*s*α)+c3*(-1.2836432242168526*^-10+(6.17432390848306*^-17+
(2.1436841844421444*^-13+2.567286448433705*^-10*s)*s)*α))*Cosh[c1/2]+c1*(c3*
(5.27375699036236*^-17+s*(-415.90704127644807+498092.2650017341*s))*α+s*
(-498092.2650017341-0.10770000000000003*α)*α-1.*c4*s*α^2*Cos[c2]+c2*
(-5.359210461105361*^-14-6.418216121084263*^-11*s)*(c3+s*α)*Sin[c2])*Sinh[c1/2])/(α*
(1.*c3*c4+4.6248121170077445*^6*s+1.*s*α+1.*c3*c4*Cos[c2]+c3*c4*(-1.-1.*Cos[c2])*Cosh[c1])),0.},
{
(c1*Cosh[c1/2]*(c3*(-5.27375699036236*^-17+(415.907041276448-498092.2650017341*s)*s)*
α+s*(-498092.2650017341-0.10770000000000003*α)*α-7.651109839778262*^-18*s*α^2*
Cos[c2]+c2*(5.35921046110536*^-14+6.418216121084263*^-11*s)*(c3+s*α)*Sin[c2])+
(α*(5.014231344597082*^-13-4.6248121170077445*^6*s+1.1954859124653534*^-19*
α-0.9999999999999998*s*α)+c3*(1.2836432242168526*^-10+2.775557561562891*^-17*α-
2.567286448433705*^-10*s^2*α))*Sinh[c1/2])/(α*(4.6248121170077445*^6*c3*c5+
4.6248121170077445*^6*s+1.*s*α+4.6248121170077445*^6*c3*c5*Cos[c2]+c3*c5*
(4.6248121170077445*^6+4.6248121170077445*^6*Cos[c2])*Cosh[c1])),
((1.*c3*c6+s*(4.6248121170077445*^6+1.*α)+1.*c3*c6*Cos[c2])*Cosh[c1/2])/
(1.*c3*c4+4.6248121170077445*^6*s+1.*s*α+1.*c3*c4*Cos[c2]+c3*c4*(1.+1.*Cos[c2])*
Cosh[c1]),(c1*Cosh[c1/2]*(c3*(-5.27375699036236*^-17+(415.907041276448-
498092.2650017341*s)*s)*α+s*(498092.2650017341+0.10770000000000003*α)*α+
4.6248121170077445*^6*c5*s*α^2*Cos[c2]+c2*(5.35921046110536*^-14+
6.418216121084263*^-11*s)*(c3+s*α)*Sin[c2])+(α*(2.1436841844421449*^-13+
1.2836432242168529*^-10*s+4.6351811278100287*^-20*α+1.1725439031608844*^-16*s*α)+
c3*(1.2836432242168526*^-10+(-6.17432390848306*^-17+(-2.143684184442144*^-
13-2.567286448433705*^-10*s)*s)*α))*Sinh[c1/2])/(α*(4.6248121170077445*^6*c3*c5+
4.6248121170077445*^6*s+1.*s*α+4.6248121170077445*^6*c3*c5*Cos[c2]+c3*c5*
(4.6248121170077445*^6+4.6248121170077445*^6*Cos[c2])*Cosh[c1])),0.},
{
(((-2.1436841844421449*^-13+s*(-1.2836432242168526*^-10-1.1725439031608844*^-16*α)-
4.6351811278100287*^-20*α)*α+c3*(1.2836432242168526*^-10+(-6.17432390848306*^-17+
(-2.1436841844421444*^-13-2.567286448433705*^-10*s)*s)*α))*Cos[c2/2]+c2*Sin[c2/2]*
((c3*(5.27375699036236*^-17+s*(-415.90704127644807+498092.2650017341*s))+s*
(498092.2650017341+0.10770000000000003*α))*α+1.*c4*s*α^2*Cosh[c1]+c1*(c3*
(5.359210461105361*^-14+6.418216121084263*^-11*s)+(-5.359210461105361*^-14-
6.418216121084263*^-11*s)*s*α)*Sinh[c1]))/(α*(1.*c3*c4+4.6248121170077445*^6*s+
1.*s*α-1.*c3*c4*Cos[c2]+c3*c4*(1.-1.*Cos[c2])*Cosh[c1])),0.,
(((-5.014231344597081*^-13+s*(4.624812117007744*^6+0.9999999999999997*α)-
1.1954859124653531*^-19*α)*α+c3*(1.2836432242168526*^-10+(2.775557561562891*^-17-
2.567286448433705*^-10*s^2)*α))*Cos[c2/2]+c2*Sin[c2/2]*((c3*(5.2737569903623595*^-17+
s*(-415.90704127644807+498092.265001734*s))+s*(-498092.265001734-0.10770000000000003*
α))*α+c1*(c3*(5.35921046110536*^-14+6.418216121084263*^-11*s)+(-5.35921046110536*^-14-
6.418216121084263*^-11*s)*s*α)*Sinh[c1]))/(α*(1.*c3*c4+4.6248121170077445*^6*s+1.*
s*α-1.*c3*c4*Cos[c2]+c3*c4*(1.-1.*Cos[c2])*Cosh[c1])),((1.*c3*c6+s*
(4.6248121170077445*^6+1.*α)+1.*c3*c6*Cosh[c1])*Sin[c2/2])/(-1.*c3*c4-
4.6248121170077445*^6*s-1.*s*α+1.*c3*c4*Cos[c2]+c3*c4*(-1.+1.*Cos[c2])*Cosh[c1])},
{
(((-2.1436841844421449*^-13+s*(-1.2836432242168529*^-10-1.1725439031608844*^-16*α)-
4.6351811278100287*^-20*α)*α+c3*(1.2836432242168526*^-10+(-6.17432390848306*^-17+
(-2.143684184442144*^-13-2.567286448433705*^-10*s)*s)*α))*Sin[c2/2]+c2*Cos[c2/2]*
((c3*(-5.27375699036236*^-17+(415.907041276448-498092.2650017341*s)*s)+
s*(-498092.2650017341-0.10770000000000003*α))*α-4.6248121170077445*^6*c5*s*α^2*
Cosh[c1]+c1*(c3*(-5.35921046110536*^-14-6.418216121084263*^-11*s)+(5.35921046110536*^-14+
6.418216121084263*^-11*s)*s*α)*Sinh[c1]))/(α*(4.6248121170077445*^6*c3*c5+
4.6248121170077445*^6*s+1.*s*α+4.6248121170077445*^6*c3*c5*Cos[c2]+c3*c5*
(4.6248121170077445*^6+4.6248121170077445*^6*Cos[c2])*Cosh[c1])),0.,
(((-5.014231344597082*^-13+s*(4.6248121170077445*^6+0.9999999999999999*α)-
1.1954859124653534*^-19*α)*α+c3*(1.2836432242168526*^-10+(2.775557561562891*^-17-
2.567286448433705*^-10*s^2)*α))*Sin[c2/2]+c2*Cos[c2/2]*((c3*(-5.27375699036236*^-17+
(415.907041276448-498092.2650017341*s)*s)+s*(498092.2650017341+0.10770000000000003*α))*α+
7.651109839778262*^-18*s*α^2*Cosh[c1]+c1*(c3*(-5.35921046110536*^-14-
6.418216121084263*^-11*s)+(5.35921046110536*^-14+6.418216121084263*^-11*s)*s*α)*
Sinh[c1]))/(α*(4.6248121170077445*^6*c3*c5+4.6248121170077445*^6*s+1.*s*α+
4.6248121170077445*^6*c3*c5*Cos[c2]+c3*c5*(4.6248121170077445*^6+
4.6248121170077445*^6*Cos[c2])*Cosh[c1])),(Cos[c2/2]*(1.*c3*c6+s*
(4.6248121170077445*^6+1.*α)+1.*c3*c6*Cosh[c1]))/(1.*c3*c4+4.6248121170077445*^6*s+1.*
s*α+1.*c3*c4*Cos[c2]+c3*c4*(1.+1.*Cos[c2])*Cosh[c1])}}
POSTED BY: Bill Nelson
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