# R determinant() and det() functions – All you need to know!

Filed Under: R Programming Hey, readers! In this article, we will be majorly focusing on R determinant() and det() functions in detail.

So, let us begin!

## First, what is determinant of a matrix?

Prior to understanding about det() and determinant() functions, let us first briefly recall the concept of determinants in mathematics.

Determinants are a linear i.e. scalar representation of a matrix component. That is, it can be considered as a scalar value which is linearly composed and computed from the square matrix schema and its values.

Determinant of a matrix relates to the volume or the area enclosed y the matrix region. Further, it reflects the linear association with the matrix with in terms of scaling.

## 1. R determinant() function

R `determinant()` function calculates the determinant value for a matrix and also returns the modulus value for the determinant.

Syntax:

```determinant(matrix)
```

As a result, we obtain the below values:

1. Modulus of the determinant
2. Attribute: We can have logarithm as an optional attribute while taking modulus into consideration.
3. class: Type of the value returned.
4. Sign: The actual sign(positive or negative) of the determinant.

Example:

In the below example, we have created a 4×4 matrix using matrix() function.

Further, we have calculated the determinant of the matrix using determinant() function.

```rm(list = ls())

data <- matrix(c(1,3,5,7,9,2,6,8), 4, 4)
print(data)

determinant(data)
```

Output:

As a result, it returns the modulus value of the determinant along with the class and mathematical sign of the value. The determinant value happens to have a negative sign as shown below–

```> print(data)
[,1] [,2] [,3] [,4]
[1,]    1    9    1    9
[2,]    3    2    3    2
[3,]    5    6    5    6
[4,]    7    8    7    8
>

> determinant(data)
\$modulus
 -66.69368
attr(,"logarithm")
 TRUE

\$sign
 -1

attr(,"class")
 "det"
```

## 2. R det() function

Using `det()` function, we can determine the determinant value of a matrix at ease. That is, it returns the linear determinant value for the matrix passed to it as an argument.

Unlike determinant() function, R det() function does not return the modulus value for a matrix. It only returns the determinant score with the actual sign that is associated with it.

Example:

In this example, it returns the determinant of the matrix using det() function.

```rm(list = ls())

data <- matrix(c(1,3,5,7,9,2,6,8), 4, 4)
print(data)

det(data)
```

Output:

```> print(data)
[,1] [,2] [,3] [,4]
[1,]    1    9    1    9
[2,]    3    2    3    2
[3,]    5    6    5    6
[4,]    7    8    7    8
>
> det(data)
 -1.084684e-29
```

To add, both determinant() and det() function takes logarithm argument into the account as a default value i.e. set to TRUE.

Thus, by default, det() and determinant() function returns the logarithm value of the determinant as a result. To which determinant() function performs modulus on!

When set to False, the actual determinant value is taken into the account as output.

## Conclusion

By this, we have come to the end of this topic. Feel free to comment below, in case you come across any question.

For more such posts related to R programming, stay tuned with us.

Till then, Happy Learning!! 🙂

## References

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