# Det in Mathematica

1. Mar 23, 2010

### EngWiPy

Hello,

I have the following code in Mathematica:

Code (Text):
G[k_, l_] :=
MatrixForm[Table[If[i == j, 1, 0], {i, 1, 3}, {j, 1, 3}]];

Print[\!$$\*UnderoverscriptBox[\(\[Sum]$$, $$k = 1$$, $$3$$]$$\*UnderoverscriptBox[\(\[Sum]$$, $$l = 1$$, $$3$$]Det[G[k, l]]\)\)];

but it does not evaluate the determinant as a number, how to force it to do that?

2. Mar 23, 2010

### Hepth

Get rid of that "MatrixForm". A table is by definition a matrix, the matrixform just changes display type. So you're operating on a display object rather than a mathematical object.

Then it works.

Remember also the way you have it, k and l are NOT the indices of the matrix. So those sums are just going to give you 9.

G[k_, l_] :=
Table[If[i == j, 1, 0], {i, 1, 3}, {j, 1, 3}][[k]][[l]];

would give you an indexable matrix but then you cannot operate on it like a matrix (det wont work). You'd have to male it a table again:
Det[Table[G[i, j], {i, 1, 3}, {j, 1, 3}]]

3. Mar 23, 2010

### EngWiPy

Yes, I know that the equations do not make sense, it is complicated to explain. But it is working now. The actual code is here, which gives an error (why?) and a very large number (not expected, I guess)!!:

Code (Text):

P = {1.6, 1.8, 2};
p = 1;
f1[k_, l_, i_, j_] := Gamma[4]*\!$$\*UnderoverscriptBox[\(\[Sum]$$, $$m = 0$$, $$3$$]
\*FractionBox[$$1$$, $$m!$$]*NIntegrate[
\*SuperscriptBox[$$Log[1 + p*y]$$, $$2$$]*
\*SuperscriptBox[$$y$$, $$3 - j$$]*Exp[$$-y$$]*
\*SuperscriptBox[$$( \*FractionBox[\(1$$, $$P[\([$$$$i$$$$]$$] + y\)])\), $$-\((3 + 1 - m)$$\)], {y, 0, Infinity}]\);
f2[k_, l_, i_, j_] := If[j == k, f3[k, l, i, j], f4[k, l, i, j]];
f3[k_, l_, i_, j_] :=
Exp[1/P[[i]]]*
NIntegrate[(Log[1 + (p*u)]*u^(3 - j))/(1/(P[[i]] + u))^(3 + 1)*
Gamma[3 + 1, 1/(P[[i]]*u)], {u, 0, Infinity}];
f4[k_, l_, i_, j_] :=
N[Gamma[3 - j + 1]*Exp[1/P[[i]]]*P[[i]]^j*Gamma[j, 1/P[[i]]]];
G[k_, l_] :=
Table[If[k == l == j, f1[k, l, i, j], f2[k, l, i, j]], {i, 1,
3}, {j, 1, 3}];

Print[\!$$\*UnderoverscriptBox[\(\[Sum]$$, $$k = 1$$, $$3$$]$$\*UnderoverscriptBox[\(\[Sum]$$, $$l = 1$$, $$3$$]Det[G[k, l]]\)\)];

Best regards