when one of element in matrix s variable below code is very slow

MA := MatrixMatrixMultiply(InputMatrix3aa - lambda*IdentityMatrix(3);
eignvalues1 := evalf(solve(Determinant(MA), lambda));
MA1 := MatrixMatrixMultiply(InputMatrix3aa - eignvalues1[1]*IdentityMatrix(3);
MA2 := MatrixMatrixMultiply(InputMatrix3aa - eignvalues1[2]*IdentityMatrix(3);
MA3 := MatrixMatrixMultiply(InputMatrix3aa - eignvalues1[3]*IdentityMatrix(3);
eignvector1 := LinearSolve(MA1,<x,y,z>);

eignvector2 := LinearSolve(MA2,<x,y,z>);

eignvector3 := LinearSolve(MA3,<x,y,z>);

m1 := <Old_Asso_eigenvector[2][1][1],Old_Asso_eigenvector[2][1][2],Old_Asso_eigenvector[2][1][3]>;
m2 := <Old_Asso_eigenvector[2][2][1],Old_Asso_eigenvector[2][2][2],Old_Asso_eigenvector[2][2][3]>;
m3 := <Old_Asso_eigenvector[2][3][1],Old_Asso_eigenvector[2][3][2],Old_Asso_eigenvector[2][3][3]>;

m1 := <Old_Asso_eigenvector[2][1][1],Old_Asso_eigenvector[2][2][1],Old_Asso_eigenvector[2][3][1]>;
m2 := <Old_Asso_eigenvector[2][1][2],Old_Asso_eigenvector[2][2][2],Old_Asso_eigenvector[2][3][2]>;
m3 := <Old_Asso_eigenvector[2][1][3],Old_Asso_eigenvector[2][2][3],Old_Asso_eigenvector[2][3][3]>;
ord := GramSchmidt([m1, m2, m3]);
ord := Basis([m1, m2, m3]);

ord[1].ord[2];  # expect = 1
ord[1].ord[3];  # expect = 1
ord[2].ord[1];  # expect = 1
ord[2].ord[3];  # expect = 1
ord[3].ord[1];  # expect = 1
ord[3].ord[2];  # expect = 1

is there a function get orthonormal basis ?

1.

assume there are 3 real number or floating number a, b, c

how to find the w and phi in 

a = sin(w*t1 + phi)

b = sin(w*t2 + phi)

c = sin(w*t3 + phi)

where w and phi are the same in above 3 equations, only different in t1, t2, t3

2.

same as above , how to find w, apha and beta in below if there are a, b, c

a = alpha*cos(w*t) + beta*sin(w*t)

b = alpha*cos(w*t) + beta*sin(w*t)

c = alpha*cos(w*t) + beta*sin(w*t)

assume there is vector a,b,c and d which are real number or floating number

how to express a in linear combination of b ,c and d

in another words, how to find coefficient m1, m2, m3

in a = m1*b + m2*c + m3*d

 can LinearSolve do this?

are these quations in wave form for harmonic ocillator?

i can not plot them

plot(exp(I*2*t) - exp(-I*2*t), t=0..10);

plot(cos(t) - I*sin(t), t=0..10);

why same solution but their plot graph are different?

plot(cos(t) + sin(t), t=0..10);
complexplot(exp(I*t), t=0..10);