FirstEigenVector := Matrix(3, 1, {(1, 1) = -.736895432967255+0.*I, (2, 1) = -.588906969844997+0.*I, (3, 1) = -.331924240964690+0.*I});
SecondEigenVector := Matrix(3, 1, {(1, 1) = -.589856901397123+0.*I, (2, 1) = .320280857681335+0.*I, (3, 1) = .741275257969058+0.*I});
ThirdEigenVector := Matrix(3, 1, {(1, 1) = .330233185410229+0.*I, (2, 1) = -.742030156443046+0.*I, (3, 1) = .583384341736151+0.*I});
LHS := ProjOfEigenVector;
LHS := Matrix(3, 3, {(1, 1) = -.736895432967255+0.*I, (1, 2) = -.589856901397123+0.*I, (1, 3) = .330233185410229+0.*I, (2, 1) = -.588906969844997+0.*I, (2, 2) = .320280857681335+0.*I, (2, 3) = -.742030156443046+0.*I, (3, 1) = -.331924240964690+0.*I, (3, 2) = .741275257969058+0.*I, (3, 3) = .583384341736151+0.*I});
RHS := c1*FirstEigenVector+c2*SecondEigenVector+c3*ThirdEigenVector;
RHS := Matrix(3, 1, {(1, 1) = (-.736895432967255+0.*I)*c1+(-.589856901397123+0.*I)*c2+(.330233185410229+0.*I)*c3, (2, 1) = (-.588906969844997+0.*I)*c1+(.320280857681335+0.*I)*c2+(-.742030156443046+0.*I)*c3, (3, 1) = (-.331924240964690+0.*I)*c1+(.741275257969058+0.*I)*c2+(.583384341736151+0.*I)*c3});
solve([LHS[1][1] = RHS[1][1], LHS[2][2] = RHS[2][1], c1^2+c2^2+c3^2 = 1], [c1, c2, c3]);

after calculated the projection matrix, 

it is a 3*3 matrix on left hand side

however, combination of eigenvectors on right hand side is 3*1 matrix

when calculated c1,c2,c3 under the condition c1^2+c2^2+c3^2 = 1

how to know whether LHS[1][1] = RHS[1][1], or LHS[1][2] = RHS[1][1] or

LHS[1][3] = RHS[1][1]

How to create a borel set from a list of decimal

if i interpolate three decimal number and solve it, 

if any number substitute into this result which is a inverse function, can the results be said borel set?

with(LinearAlgebra):
t:=1;
NewMatrix3 := Matrix([[test10, close3(t) , close3(t+1)],
[close3(t) , close3(t+1) ,0],
[close3(t+1) , 0,0]]);

Matrix(3, 3, {(1, 1) = test10, (1, 2) = 5.59, (1, 3) = 5.74, (2, 1) = 5.59, (2, 2) = 5.74, (2, 3) = 0, (3, 1) = 5.74, (3, 2) = 0, (3, 3) = 0})

NewEigenMatrix := Eigenvalues(NewMatrix3);
solve([MatrixMatrixMultiply(NewMatrix3,Matrix([[x],[y],[z]]))[1][1] = NewEigenMatrix[1]* Matrix([[x],[y],[z]])[1][1],
MatrixMatrixMultiply(NewMatrix3,Matrix([[x],[y],[z]]))[2][1] = NewEigenMatrix[1]* Matrix([[x],[y],[z]])[2][1],
MatrixMatrixMultiply(NewMatrix3,Matrix([[x],[y],[z]]))[3][1] = NewEigenMatrix[1]* Matrix([[x],[y],[z]])[3][1]]
, [x,y,z]);

k := a*x6^7 + b*x6^6 + c*x6^5 + d*x6^4 + e*x6^3 + f*x6^2 + g*x6;
discrim(k, x6);

after know the discriminant equation, how to do next?

solve(Max(Min(x, 1), Min(x, 2)));
solve(Min(Max(x, 1), Max(x, 2)));

i do not know how to use Rootof something

any other expression