# Det: Determinant of a Square Matrix In matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

## Description

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

 ```1 2``` ```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 `...` arguments passed to `gaussianElimination` or `Eigen`

## Value

the determinant of `X`

## Author(s)

John Fox

`det` for the base R function

`gaussianElimination`, `Eigen`

Other determinants: `adjoint`, `cofactor`, `minor`, `rowCofactors`, `rowMinors`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```A <- matrix(c(1,2,3,2,5,6,3,6,10), 3, 3) # nonsingular, symmetric A Det(A) Det(A, verbose=TRUE, fractions=TRUE) B <- matrix(1:9, 3, 3) # a singular matrix B Det(B) C <- matrix(c(1, .5, .5, 1), 2, 2) # square, symmetric, nonsingular Det(C) Det(C, method="eigenvalues") Det(C, method="cofactors") ```

matlib documentation built on April 4, 2018, 5:03 p.m.