Cross product of transpose of matrix in R
Cross product of transpose of matrix in R, you’ll learn how to calculate matrix cross products using the crossprod and tcrossprod functions.
The cross product of a matrix and its transpose is a fundamental concept in linear algebra, and it is often used in various applications such as machine learning, data analysis, and statistics.
In R, the cross product of a matrix and its transpose can be calculated using the tcrossprod() function, which is a more efficient and convenient way to compute the result compared to using the t() function and the %*% operator.
We will also provide examples of how to use this function in practice, and discuss the advantages and by the end of this tutorial, you will have a solid understanding of how to calculate the cross product of a matrix and its transpose in R, and how to apply this knowledge in your own projects.
Example 1: Cross Product Using crossprod Function
Create example data:
my_mat <- matrix(1:9, nrow = 3)
my_mat
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 2 5 8
[3,] 3 6 9
my_vec <- 1:3Calculate cross product using crossprod function:
my_crossprod1 <- crossprod(my_mat, my_vec)
my_crossprod1Result:
[,1]
[1,] 14
[2,] 32
[3,] 50Example 2: Cross Product of Transpose of Matrix Using tcrossprod Function
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Calculate cross product of transpose of matrix using tcrossprod function:
my_tcrossprod1 <- tcrossprod(my_mat)
my_tcrossprod1Result:
[,1] [,2] [,3]
[1,] 66 78 90
[2,] 78 93 108
[3,] 90 108 126Note that the same result can be obtained using the %*% operator and t function:
my_tcrossprod2 <- my_mat %*% t(my_mat)
my_tcrossprod2Result:
[,1] [,2] [,3]
[1,] 66 78 90
[2,] 78 93 108
[3,] 90 108 126
