Matrices

Matrices in Python

A matrix is a 2D array of numbers with $m$ rows and $n$ columns — an $m imes n$ matrix. In Python, we represent it as a list of lists.

A = [[1, 2, 3],
     [4, 5, 6]]

print(A)           # [[1, 2, 3], [4, 5, 6]]
print(len(A))      # 2  — rows
print(len(A[0]))   # 3  — columns
print(A[0][1])     # 2  — row 0, column 1
print(A[1])        # [4, 5, 6] — entire row 1

Special Matrices

# Zeros matrix (3×4)
zeros = [[0]*4 for _ in range(3)]

# Identity matrix (3×3)
I = [[1 if i == j else 0 for j in range(3)] for i in range(3)]
# [[1, 0, 0],
#  [0, 1, 0],
#  [0, 0, 1]]

The Identity Matrix

The identity matrix $I$ is the matrix equivalent of the number 1: $mathbf{A} cdot I = mathbf{A}$ for any matrix $mathbf{A}$. It has 1s on the diagonal and 0s everywhere else.

Your Task

Implement identity(n) that returns the $n imes n$ identity matrix as a list of lists.