Ruang Eigen

library(Matrix)

library(ggplot2)

A <- matrix(c(1, 2, 3, 4), nrow = 2, ncol = 2)

eigen_result <- eigen(A)

diagonal_matrix <- diag(eigen_result$values)

eigenvector_df <- data.frame(x = c(0, eigen_result$vectors[1, 1]),
                             y = c(0, eigen_result$vectors[2, 1]))

eigenvector_plot <- ggplot(eigenvector_df, aes(x = x, y = y)) +
  geom_segment(aes(xend = x, yend = y), arrow = arrow(length = unit(0.3, "cm"))) +
  xlim(-1, 1) + ylim(-1, 1) +
  theme_minimal()

diagonalization_df <- data.frame(x = c(0, eigen_result$vectors[1, 1], 0, eigen_result$vectors[1, 2]),
                                 y = c(0, eigen_result$vectors[2, 1], 0, eigen_result$vectors[2, 2]))

diagonalization_plot <- ggplot(diagonalization_df, aes(x = x, y = y)) +
  geom_segment(aes(xend = x, yend = y), arrow = arrow(length = unit(0.3, "cm"))) +
  xlim(-1, 1) + ylim(-1, 1) +
  theme_minimal()

print("Eigenvalues:")

## [1] "Eigenvalues:"

print(eigen_result$values)

## [1]  5.3722813 -0.3722813

print("Eigenvectors:")

## [1] "Eigenvectors:"

print(eigen_result$vectors)

##            [,1]       [,2]
## [1,] -0.5657675 -0.9093767
## [2,] -0.8245648  0.4159736

print("Diagonal Matrix:")

## [1] "Diagonal Matrix:"

print(diagonal_matrix)

##          [,1]       [,2]
## [1,] 5.372281  0.0000000
## [2,] 0.000000 -0.3722813

print("Plot Eigenvectors:")

## [1] "Plot Eigenvectors:"

print(eigenvector_plot)

print("Plot Diagonalization:")

## [1] "Plot Diagonalization:"

print(diagonalization_plot)