Special Matrices

# Identity Matrix

# Creates a 3x3 identity matrix
I3 = Matrix{Float64}(I, 3, 3)  # Explicitly specifying the type and size
println("3x3 Identity Matrix:\n", I3)

I4 = Diagonal(ones(4)) # Another way to create a 4x4 identity matrix
println("\n4x4 Identity Matrix (using Diagonal):\n", I4)


# Zero Matrix

# Creates a 2x4 zero matrix of Float64s
Z24 = zeros(Float64, 2, 4)
println("\n2x4 Zero Matrix:\n", Z24)

# Creates a 3x3 zero matrix of Ints (Julia defaults to Int if not specified)
Z33_int = zeros(Int, 3, 3)
println("\n3x3 Zero Matrix (Integers):\n", Z33_int)


# One Matrix

# Creates a 3x2 matrix of ones (Float64 by default)
O32 = ones(3, 2)
println("\n3x2 One Matrix:\n", O32)

# Creates a 4x4 matrix of ones (Integers)
O44_int = ones(Int, 4, 4)
println("\n4x4 One Matrix (Integers):\n", O44_int)


# Matrix of a specific value

# Creating a 5x5 matrix filled with the value 7.
M55_7 = fill(7.0, 5, 5) # Float64
println("\n5x5 Matrix filled with 7.0:\n", M55_7)

M23_neg5 = fill(-5, 2, 3)  # Int
println("\n2x3 Matrix filled with -5:\n", M23_neg5)


# Important Considerations and Best Practices:

# Type Stability: It's generally good practice to specify the element type of your matrices (e.g., Float64, Int). This improves performance, especially for larger matrices.
# Size: Be explicit about the dimensions of your matrices.
# `Matrix{}(I, n, n)`: This is a concise and efficient way to create an identity matrix of size `n x n` and a specified type.
# `Diagonal(ones(n))`:  A very efficient way to create an identity matrix, especially for larger sizes.
# `zeros()` and `ones()`: Use these functions to create matrices of zeros and ones, respectively.  Specify the type if needed.
# `fill(value, rows, cols)`: Use this to create a matrix where all elements have the same specified value.
# Printing: The `println()` function is used here for demonstration.  In more complex programs, you might use other methods for displaying or working with matrices.