Response to Laura Puebla - Small differences in code:

# Defining the matrix C
C <- matrix(c(-1, 2, -6, 6), nrow = 2, byrow = TRUE)

# Computing the eigenvalues and eigenvectors
eigen_result <- eigen(C)

# Extracting eigenvalues and eigenvectors
eigenvalues <- eigen_result$values
eigenvectors <- eigen_result$vectors

# Computing algebraic multiplicities
algebraic_multiplicities <- table(round(eigenvalues, 5))

# Computing geometric multiplicities
geometric_multiplicities <- sapply(1:length(eigenvalues), function(i) sum(abs(eigenvalues[i] - eigen(C)$values) < 1e-10))

# Displaying the results
print("Eigenvalues:")

## [1] "Eigenvalues:"

print(eigenvalues)

## [1] 3 2

print("Eigenvectors:")

## [1] "Eigenvectors:"

print(eigenvectors)

##            [,1]       [,2]
## [1,] -0.4472136 -0.5547002
## [2,] -0.8944272 -0.8320503

print("Algebraic Multiplicities:")

## [1] "Algebraic Multiplicities:"

print(algebraic_multiplicities)

## 
## 2 3 
## 1 1

print("Geometric Multiplicities:")

## [1] "Geometric Multiplicities:"

print(geometric_multiplicities)

## [1] 1 1