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
determinant() function calculates the determinant value for a matrix and also returns the modulus value for the determinant.
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.
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)
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
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.
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)
> 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.
By this, we have come to the end of this topic. Feel free to comment below, in case you come across any question.
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Till then, Happy Learning!! 🙂