Determinant of a matrix

ALGORITHM
The determinant of an LU decomposed matrix is the product of the diagonal elements. We can easy compute the determinant of a given matrix A. by LUDCMP function.

IMPLEMENTATION
Unit: fragment of a program
 
Interface: LUDCMP
 
Result: the program displays the value of the determinant
 


/* read an input N by N matrix A. */
...
D = LUDCMP(N)
do J = 1 to N; D = D * A.J.J; end
say "Determinant =" D

 

EXAMPLE
The determinant of the input matrix A. (Combinatorial matrix)

 


A. = Y
do J = 1 to N
  A.J.J = X + Y
end

 

is equal (X+N*Y)*X**(N-1). Computation of determinant for N=100, X=1, Y=2 and numeric digits 9 requires 17.57 seconds. The result is

Determinant = 201.001499

CONNECTIONS
Linear Algebraic Equations
     Inverse of a matrix
     LU decomposition
     Solution of linear algebraic equations

Literature
Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical Recipes in C : the art of scientific computing
- 2nd ed. University Press, Cambridge, 1992
Faddejev A.K., Sominskij J.S. Sbornik zadac po vyssej algebre
Nauka, Moskva 1964


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last modified 1st August 2001
Copyright © 2000-2001 Vladimir Zabrodsky
Czech Republic