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

So, let us begin!

Table of Contents

## 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:

**Modulus of the determinant****Attribute**: We can have logarithm as an optional attribute while taking modulus into consideration.**class**: Type of the value returned.**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
[1] -66.69368
attr(,"logarithm")
[1] TRUE
$sign
[1] -1
attr(,"class")
[1] "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] -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!! 🙂