MATLAB Function Reference |

**Syntax**

**Description**

```
d = det(X)
```

returns the determinant of the square matrix `X`

. If `X`

contains only integer entries, the result `d`

is also an integer.

**Remarks**

Using `det(X)`

`==`

`0`

as a test for matrix singularity is appropriate only for matrices of modest order with small integer entries. Testing singularity using `abs(det(X))`

`<=`

`tolerance`

is not recommended as it is difficult to choose the correct tolerance. The function `cond(X)`

can check for singular and nearly singular matrices.

**Algorithm**

The determinant is computed from the triangular factors obtained by Gaussian elimination

**Examples**

The statement `A = [1 2 3; 4 5 6; 7 8 9]`

This happens to be a singular matrix, so `d = det(A)`

produces `d = 0. `

Changing `A(3,3)`

with `A(3,3) = 0 `

turns `A`

into a nonsingular matrix. Now `d = det(A) `

produces `d = 27`

.

**See Also**

The arithmetic operators `\`

, `/`

depfun | detrend |

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