Determinant of a Square Matrix

Returns the determinant of a square matrix X, computed either by Gaussian elimination, expansion by cofactors, or as the product of the eigenvalues of the matrix. If the latter, X must be symmetric.

Usage

Det(
  X,
  method = c("elimination", "eigenvalues", "cofactors"),
  verbose = FALSE,
  fractions = FALSE,
  ...
)

Arguments

X

a square matrix

method

one of `"elimination"` (the default), `"eigenvalues"`, or `"cofactors"` (for computation by minors and cofactors)

verbose

logical; if TRUE, print intermediate steps

fractions

logical; if TRUE, try to express non-integers as rational numbers, using the fractions function; if you require greater accuracy, you can set the cycles (default 10) and/or max.denominator (default 2000) arguments to fractions as a global option, e.g., options(fractions=list(cycles=100, max.denominator=10^4)).

...

arguments passed to gaussianElimination or Eigen

Value

the determinant of X

See also

det for the base R function

gaussianElimination, Eigen

Other determinants: adjoint(), cofactor(), minor(), rowCofactors(), rowMinors()

Author

John Fox

Examples

A <- matrix(c(1,2,3,2,5,6,3,6,10), 3, 3) # nonsingular, symmetric
A
#>      [,1] [,2] [,3]
#> [1,]    1    2    3
#> [2,]    2    5    6
#> [3,]    3    6   10
Det(A)
#> [1] 1
Det(A, verbose=TRUE, fractions=TRUE)
#> 
#> Initial matrix:
#> Warning: Function is deprecated. See latexMatrix() and Eqn() for more recent approaches
#>      [,1] [,2] [,3]
#> [1,]  1    2    3  
#> [2,]  2    5    6  
#> [3,]  3    6   10  
#> 
#> row: 1 
#> 
#>  exchange rows 1 and 3 
#> Warning: Function is deprecated. See latexMatrix() and Eqn() for more recent approaches
#>      [,1] [,2] [,3]
#> [1,]  3    6   10  
#> [2,]  2    5    6  
#> [3,]  1    2    3  
#> 
#>  multiply row 1 by 1/3 
#> Warning: Function is deprecated. See latexMatrix() and Eqn() for more recent approaches
#>      [,1] [,2] [,3]
#> [1,]    1    2 10/3
#> [2,]    2    5    6
#> [3,]    1    2    3
#> 
#>  multiply row 1 by 2 and subtract from row 2 
#> Warning: Function is deprecated. See latexMatrix() and Eqn() for more recent approaches
#>      [,1] [,2] [,3]
#> [1,]    1    2 10/3
#> [2,]    0    1 -2/3
#> [3,]    1    2    3
#> 
#>  subtract row 1 from row 3 
#> Warning: Function is deprecated. See latexMatrix() and Eqn() for more recent approaches
#>      [,1] [,2] [,3]
#> [1,]    1    2 10/3
#> [2,]    0    1 -2/3
#> [3,]    0    0 -1/3
#> 
#> row: 2 
#> 
#>  multiply row 2 by 2 and subtract from row 1 
#> Warning: Function is deprecated. See latexMatrix() and Eqn() for more recent approaches
#>      [,1] [,2] [,3]
#> [1,]    1    0 14/3
#> [2,]    0    1 -2/3
#> [3,]    0    0 -1/3
#> 
#> row: 3 
#> 
#>  multiply row 3 by -3 
#> Warning: Function is deprecated. See latexMatrix() and Eqn() for more recent approaches
#>      [,1] [,2] [,3]
#> [1,]    1    0 14/3
#> [2,]    0    1 -2/3
#> [3,]    0    0    1
#> 
#>  multiply row 3 by 14/3 and subtract from row 1 
#> Warning: Function is deprecated. See latexMatrix() and Eqn() for more recent approaches
#>      [,1] [,2] [,3]
#> [1,]    1    0    0
#> [2,]    0    1 -2/3
#> [3,]    0    0    1
#> 
#>  multiply row 3 by 2/3 and add to row 2 
#> Warning: Function is deprecated. See latexMatrix() and Eqn() for more recent approaches
#>      [,1] [,2] [,3]
#> [1,] 1    0    0   
#> [2,] 0    1    0   
#> [3,] 0    0    1   
#> 
#>  det = (-1)^1 x 3 x 1 x -1/3 = 1
B <- matrix(1:9, 3, 3) # a singular matrix
B
#>      [,1] [,2] [,3]
#> [1,]    1    4    7
#> [2,]    2    5    8
#> [3,]    3    6    9
Det(B)
#> [1] 0
C <- matrix(c(1, .5, .5, 1), 2, 2) # square, symmetric, nonsingular
Det(C)
#> [1] 0.75
Det(C, method="eigenvalues")
#> [1] 0.75
Det(C, method="cofactors")
#> [1] 0.75