Det {lazy.symbolic} R Documentation

## Determinant of a Symbolic Matrix by Sweeping

### Description

Determinant of a Symbolic Matrix by Sweeping

### Usage

```Det(A, loc = 1:nrow(A), log = 0, simplify = 1, debug = 0)
```

### Arguments

 `A` A square matrix `loc` vector of pivot locations `log` = 1 to calculate log determinant `simplify` = 0 not to use Simplify nor remove_paren = 1 to use Simplify `debug` = 1 to print details

### Details

Definition of Sweep Operator
C <- matSweep( A, p ) means:

``` c[i,j] <- c[i,j] - c[i,p]*c[p,j]/c[p,p]
c[p,] <- c[p,]/c[p,p]
c[,p] <- - c[,p]/c[p,p]
```

# Inversion of A.
matSweep( A, 1:ncol(A) ) == solve(A)
This is equivalent to Inv(A).

The determinant of A is given as the product of all the pivots, c[p,p], when inverting A using sweep operator.

### Value

The determinant of A

### Examples

```
# determinant of 2 x 2 A
A <- demomat(2,2,root="a")
Det(A)
Simplify(Expand(lv()))
Det(A,log=1)

# n x n (slow!)
set.seed(1701)
n=3
B <- demomat(n,n,root="b")
dd <- Det(B)
Bn <- matrix(runif(n*n),n)
Print(Eval(dd,B=Bn),det(Bn))

Expand(dd); Expand(lv()); Expand(lv()); Expand(lv())
ddd <- lv()
Print( Eval(ddd,B=Bn),det(Bn) )

```

[Package lazy.symbolic version 0.1.3 Index]