Matrices

Zero-dependency Python snippets for matrix operations using the standard library (lists of lists, no numpy).

10 snippets available in this sub-category.

---

Simple

Matrix creation and display

math matrix create display

Create and display matrices

def create_matrix(rows, cols, fill=0):
    """Create a matrix (list of lists) with given dimensions and fill value."""
    return [[fill for _ in range(cols)] for _ in range(rows)]


def print_matrix(matrix):
    """Pretty-print a matrix."""
    for row in matrix:
        print(" ".join(str(x) for x in row))


# Examples
m = create_matrix(2, 3, 1)
print_matrix(m)
# 1 1 1
# 1 1 1

Notes

• Uses lists of lists
• No external libraries

---

Matrix addition and subtraction

math matrix add subtract

Add and subtract matrices

def add_matrices(a, b):
    """Add two matrices elementwise."""
    return [[x + y for x, y in zip(row_a, row_b)] for row_a, row_b in zip(a, b)]


def subtract_matrices(a, b):
    """Subtract two matrices elementwise."""
    return [[x - y for x, y in zip(row_a, row_b)] for row_a, row_b in zip(a, b)]


# Examples
A = [[1, 2], [3, 4]]
B = [[5, 6], [7, 8]]
print(add_matrices(A, B))  # [[6, 8], [10, 12]]
print(subtract_matrices(A, B))  # [[-4, -4], [-4, -4]]

Notes

• Matrices must be same size
• No error checking for mismatched sizes

---

Matrix multiplication (dot product)

math matrix multiply dot-product

Multiply matrices (dot product)

def create_matrix(rows, cols, fill=0):
    # Function is defined in one of the above code block
    pass

def multiply_matrices(a, b):
    """Multiply two matrices (dot product)."""
    result = create_matrix(len(a), len(b[0]))
    for i in range(len(a)):
        for j in range(len(b[0])):
            result[i][j] = sum(a[i][k] * b[k][j] for k in range(len(b)))
    return result


# Examples
A = [[1, 2], [3, 4]]
B = [[2, 0], [1, 2]]
print(multiply_matrices(A, B))  # [[4, 4], [10, 8]]

Notes

• Number of columns in A must equal rows in B
• No error checking for mismatched sizes

---

Matrix transpose

math matrix transpose

Transpose a matrix

def transpose_matrix(matrix):
    """Transpose a matrix (swap rows and columns)."""
    return [list(row) for row in zip(*matrix)]


# Examples
A = [[1, 2, 3], [4, 5, 6]]
print(transpose_matrix(A))  # [[1, 4], [2, 5], [3, 6]]

Notes

• Uses zip and unpacking
• Returns new matrix

---

Complex

Identity, zero, and diagonal matrices

math matrix identity zero diagonal

Create special matrices

def create_matrix(rows, cols, fill=0):
    # Function is defined in one of the above code block
    pass

def identity_matrix(n):
    """Create an n x n identity matrix."""
    return [[1 if i == j else 0 for j in range(n)] for i in range(n)]


def zero_matrix(rows, cols):
    """Create a zero matrix."""
    return create_matrix(rows, cols, 0)


def diagonal_matrix(diag):
    """Create a diagonal matrix from a list of diagonal elements."""
    n = len(diag)
    return [[diag[i] if i == j else 0 for j in range(n)] for i in range(n)]


# Examples
print(identity_matrix(3))  # [[1,0,0],[0,1,0],[0,0,1]]
print(zero_matrix(2, 2))  # [[0,0],[0,0]]
print(diagonal_matrix([1, 2, 3]))  # [[1,0,0],[0,2,0],[0,0,3]]

Notes

• Useful for linear algebra
• Diagonal from list

---

Determinant (2x2, 3x3)

math matrix determinant 2x2 3x3

Compute determinant (2x2, 3x3)

def determinant_2x2(m):
    """Determinant of a 2x2 matrix."""
    return m[0][0] * m[1][1] - m[0][1] * m[1][0]


def determinant_3x3(m):
    """Determinant of a 3x3 matrix."""
    return (
        m[0][0] * m[1][1] * m[2][2]
        + m[0][1] * m[1][2] * m[2][0]
        + m[0][2] * m[1][0] * m[2][1]
        - m[0][2] * m[1][1] * m[2][0]
        - m[0][0] * m[1][2] * m[2][1]
        - m[0][1] * m[1][0] * m[2][2]
    )


# Examples
M2 = [[1, 2], [3, 4]]
M3 = [[6, 1, 1], [4, -2, 5], [2, 8, 7]]
print(determinant_2x2(M2))  # -2
print(determinant_3x3(M3))  # -306

Notes

• Only for 2x2 and 3x3
• For larger, use recursion or libraries

---

Inverse (2x2)

math matrix inverse 2x2

Compute inverse (2x2)

def determinant_2x2(m):
    # Function is defined in one of the above code block
    pass

def inverse_2x2(m):
    """Inverse of a 2x2 matrix."""
    det = determinant_2x2(m)
    if det == 0:
        raise ValueError("Singular matrix")
    return [[m[1][1] / det, -m[0][1] / det], [-m[1][0] / det, m[0][0] / det]]


# Examples
M = [[4, 7], [2, 6]]
print(inverse_2x2(M))  # [[0.6, -0.7], [-0.2, 0.4]]

Notes

• Only for 2x2
• Raises error if singular

---

Edge Cases

Handle invalid matrices

math matrix error-handling edge-case

Robust matrix operations

def add_matrices(a, b):
    # Function is defined in one of the above code block
    pass

def safe_add_matrices(a, b):
    """Add matrices, return None on error."""
    try:
        return add_matrices(a, b)
    except Exception as e:
        print(f"Error: {e}")
        return None


# Examples
print(safe_add_matrices([[1, 2]], [[1, 2], [3, 4]]))  # Error, returns None

Notes

• Handles mismatched sizes
• Returns None or error

---

Performance comparison

math matrix performance benchmarking

Benchmark matrix operations

import time


def create_matrix(rows, cols, fill=0):
    # Function is defined in one of the above code block
    pass

def add_matrices(a, b):
    # Function is defined in one of the above code block
    pass

def benchmark_matrix_addition():
    """Benchmark matrix addition."""
    n = 1000
    A = create_matrix(n, n, 1)
    B = create_matrix(n, n, 2)
    start = time.time()
    add_matrices(A, B)
    print(f"Addition: {time.time() - start:.6f}s")


# benchmark_matrix_addition()

Notes

• Matrix ops are slower than scalar
• Useful for performance-critical code

---

Practical Examples

Solving systems of equations (2x2)

math matrix solve system 2x2

Solve 2x2 linear systems

def solve_2x2(a, b, c, d, e, f):
    """Solve ax + by = e, cx + dy = f for x, y."""
    det = a * d - b * c
    if det == 0:
        raise ValueError("No unique solution")
    x = (e * d - b * f) / det
    y = (a * f - e * c) / det
    return x, y


# Examples
print(solve_2x2(2, 1, 1, -1, 1, 0))  # (1.0, -1.0)

Notes

• Only for 2x2
• Raises error if no unique solution

---

🔗 Cross-References

• Reference: See 📂 Linear Algebra
• Reference: See 📂 Vectors

🏷️ Tags

math, matrix, add, subtract, multiply, transpose, identity, zero, diagonal, determinant, inverse, solve, performance, edge-case, best-practices

📝 Notes

• Matrix Operations are Fundamental in Math and Science
• Uses Only Standard Library (No numpy)
• Handles Edge Cases and Invalid Input
• Suitable for Small to Medium Matrices