# Calculate the value of a Determinant

Posted 7 months ago
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 In Mathematica, we can find the value of a determinant by the built-in function Det, but how can I find a value of a determinant like this one? $$\left| \begin{array}{ccccc} 1 & x & x^2 & \cdots & x^{n-1} \\ 1 & a_1 & a_1^2 & \cdots & a_1^{n-1} \\ \vdots & \vdots & \vdots & & \vdots \\ 1 & a_{n-1} & a_{n-1}^2 & \cdots & a_{n-1}^{n-1} \\ \end{array} \right|$$ That seems to have some problems.
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Posted 7 months ago
 This question in vague. What "problems" are you seeing? Provide details with code.
Posted 7 months ago
 I don't know the code, I am looking for the codes which can calculate the determinant.
Posted 7 months ago
 I am afraid there is no simple closed expression for the determinant: mm[n_] := Table[If[i == 1, x^j, a[i - 1, j]^j], {i, 1, n}, {j, 0, n - 1}] mm[3] // MatrixForm Collect[Det[mm[4]], x] 
Posted 7 months ago
 It's a Vandermonde matrix. The determinant is the product of differences between elements in the second column (subtracting lower-row elements from higher.)
Posted 7 months ago
 That's true,but I want to know how can I calculate its value in Mathematica.
Posted 7 months ago
 Make your matrix mm[n_] := Table[If[i == 1, x^j, a[i - 1, i]^j], {i, 1, n}, {j, 0, n - 1}] mm[3] // MatrixForm and calculate its determinant det[m_] := Product[ (m[[j, 2]] - m[[i, 2]]), {i, 1, Length[m] - 1}, {j, i + 1, Length[m]}] Example det[mm[5]] - Det[mm[5]] // Expand The det-method is (of course) considerably faster Timing[det[mm[10]];] Timing[Det[mm[10]];] 
Posted 7 months ago
 But it can't calculate mm[n],can it?
 Are you kidding? What do you expect? The general determinant is Product [ (m[[ j, 2 ]] - m[[ i, 2 ]]), {i, 1, Length[ m ] - 1}, {j, i + 1, Length[ m ]} ] What do you want to calculate then ?You must at least specify n.