@student_md   The procedure  ModalMatrix1  returns the modal matrix of  A  and  the matrix  D  which you want :

ModalMatrix1:=proc(A)
uses LinearAlgebra;
op(simplify(fnormal~(evalf~([Eigenvectors(A)[2], DiagonalMatrix(convert(Eigenvectors(A)[1],list))])), zero));
end proc:

Examples of use:

ModalMatrix1(<-4,-2; 3,1>);
ModalMatrix1(<-4,-2,5; -2,1,7; 5,7,9>);

@toandhsp  Very strange!  Try the following variant. I think it should be working:

restart; 
L := simplify([log[2](3) = a, log[3](5) = b, log[7](2) = c, log[140](63)]); 
S := {op(op(solve(L[1 .. 3], [ln(3), ln(5), ln(7)])))}; 
simplify(eval(L[4], S));

@toandhsp 

L:=simplify([log[2](3)=a, log[3](5)=b, log[7](2)=c, log[140](63)]);
simplify(eval(L[4], {solve(L[1..3], [ln(3), ln(5), ln(7)])[ ] [ ]}));

@taro  This function  t->t="."  works properly only in the context of  select  or  remove   commands. If you use it separately, then add at the right  is  command:

f:=t->is(t="."):
f(9);

                                 false
 

@jacksonmeg   It is obvious that if your system has a solution  (c1, c2,c3, c4) , the system will also have the solution  (-c1, -c2, -c3, -c4). So everything is OK.

@jacksonmeg  You wrote  g:=subs(x=1, b) . Therefore you must solve the system  {g[1], g[2], ... } 

@jacksonmeg  You choose to every time the same system. Replace  d  by  g  and so on.

@jacksonmeg  For solving in an explicit form for  f  you can use  allvalues  command:

f := {c1 = 0, c2 = -RootOf(2*_Z^2-1), c3 = 0, c4 = RootOf(2*_Z^2-1)};

allvalues(f);

@Preben Alsholm  Here is an example of the same error in the new worksheet (I use Maple 2016.1):

@one man  In your solution not satisfied OP's condition:   "...to plot this surface with a direct mapping, that is without use of implicit plotting over a volume or rejecting grid points "

@kharonsen  Certainly possible, but you must do it yourself. You now have 2 versions: mine, in which everything is very simple and all the shifts made by one unit above or right or left, and Tom' s one that is closer to your source code. If you study these versions you can easily solve your problem. 

@ANANDMUNAGALA  If you mean a broken line in 2D or 3D  use  plottools[curve]  command.

Example (a hexagon in 3D):

plots[display](plottools[curve]([ [2,1,0], [1,2,0], [0,2,1], [0,1,2], [1,0,2], [2,0,1], [2,1,0] ]), axes=normal, color=red, thickness=3);

Addition. See also the procedure  PiecewisePlot  above which automates the plotting of a piecewise curve in 3D.

Edited.

@Scot Gould  This is probably due to some specific evaluative Maple rules.

Workaround:

restart;
z:=A*<x,y>;
plots:-fieldplot(eval(z, A=1.0), x=0..1, y=0..1);

@rlopez  It must be proven! Here's the proof in Maple:

restart;
subs(cos(theta)=x/r, sin(theta)=y/r, r=sqrt(x^2+y^2), r=3*cos(theta)-2*sin(theta));
expand(%*sqrt(x^2+y^2));
(lhs-rhs)(%)=0;
Student[Precalculus][CompleteSquare](%, x,y);  # This is the canonical equation of the circle centered at (-1,3/2) and radius sqrt(13)/2

@mnpjf  Carefully re-read this sentence:

arctan(y, x)  command returns the angle (of the range  -Pi..Pi ), which the radius vector of a point with coordinates (x, y)  forms with the positive direction of x-axis.