x̄ - > Factorization using various methods depending on the type of factorization you want to achieve.

 In R, you can perform factorization using various methods depending on the type of factorization you want to achieve. Here, I'll cover two common types: matrix factorization (for collaborative filtering, for example) and factorization of integers.

# Create a sample matrix

set.seed(123) mat <- matrix(rnorm(25), nrow = 5) # Perform Singular Value Decomposition (SVD) svd_result <- svd(mat) # Get factorized matrices U <- svd_result$u D <- diag(svd_result$d) V <- svd_result$v # Reconstruct the original matrix reconstructed_mat <- U %*% D %*% t(V) # Print the original and reconstructed matrices print("Original Matrix:") print(mat) print("Reconstructed Matrix:") print(reconstructed_mat)

# Install and load the numbers package

install.packages("numbers")

library(numbers)

# Integer to factorize

integer_to_factorize <- 84

# Find prime factors

prime_factors <- primeFactors(integer_to_factorize)

# Print the prime factors

print(paste("Prime Factors of", integer_to_factorize, ":", paste(prime_factors, collapse = ", ")))

# Factorization function

# Factorization function

factorization <- function(n) {

  # Returns a vector of prime factors of n

  result <- c()

  i <- 2

  while (i <= n) {

    if (n %% i == 0) {

      result <- c(result, i)

      n <- n / i

    } else {

      i <- i + 1

    }

  }

  return(result)

}

# Least squares example

# Assume you have a set of data points (x, y)

x <- c(1, 2, 3, 4, 5)

y <- c(2, 4, 5, 4, 5)

# Fit a linear model using least squares

fit <- lm(y ~ x)

# Print the coefficients

cat("Intercept:", coef(fit)[1], "\n")

cat("Slope:", coef(fit)[2], "\n")

# Greatest common divisor function

gcd <- function(a, b) {

  while (b != 0) {

    remainder <- a %% b

    a <- b

    b <- remainder

  }

  return(abs(a))

}

# Example of finding the GCD

num1 <- 24

num2 <- 36

result_gcd <- gcd(num1, num2)

cat("Greatest Common Divisor of", num1, "and", num2, "is:", result_gcd, "\n")

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