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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 <- 1:3

Calculate cross product using crossprod function:

my_crossprod1 <- crossprod(my_mat, my_vec)
my_crossprod1

Result:

      [,1]
[1,]   14
[2,]   32
[3,]   50

Example 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_tcrossprod1

Result:

     [,1] [,2] [,3]
[1,]   66   78   90
[2,]   78   93  108
[3,]   90  108  126

Note that the same result can be obtained using the %*% operator and t function:

my_tcrossprod2 <- my_mat %*% t(my_mat)
my_tcrossprod2

Result:

      [,1] [,2] [,3]
[1,]   66   78   90
[2,]   78   93  108
[3,]   90  108  126

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