Matrix Operations in Python
1. Matrix Operations: Addition and Subtraction
Two matrices A and B of the same shape can be added:
123456789import numpy as np A = np.array([[1, 2], [5, 6]]) B = np.array([[3, 4], [7, 8]]) C = A + B print(f'C = {C}') # C = [[4, 6], [12, 14]]
2. Matrix Multiplication Rules
Matrix multiplication is not element-wise.
Rule: if A has shape (n,m) and B has shape (m,l), then the result has shape (n,l).
123456789101112131415# Example random matrix 3x2 A = np.random.rand(3, 2) print(f'A = {A}') # Example random matrix 2x4 B = np.random.rand(2, 4) print(f'B = {B}') # product shape (3, 4) product = np.dot(A, B) print(f'np.dot(A, B) = {product}') # or equivalently product = A @ B print(f'A @ B = {product}')
3. Transpose
Transpose flips rows and columns.
General rule: if A is (n×m), then AT is (m×n).
12345A = np.array([[1, 2, 3], [4, 5, 6]]) A_T = A.T # Transpose of A print(A_T)
4. Inverse of a Matrix
A matrix A has an inverse A−1 if:
A⋅A−1=Iwhere I is the identity matrix.
Not all matrices have inverses. A matrix must be square and full-rank.
Quiz
- What does
np.linalg.inv(A)do in Python when solving the system $Ax = b$?
A) Rotates vector $x$ B) Eliminates matrix $A$ C) Reverses the linear transformation applied by $A$ D) None of the above
Correct Answer: C
Correct Answer: B
12345678A = np.array([[1, 2], [3, 4]]) A_inv = np.linalg.inv(A) # Inverse of A print(A_inv) I = np.eye(2) # Identity matrix 2x2 print(assert np.allclose(A @ A_inv, I)) # Check if product equals identity
1. What does the following Python code print?
2. In Python's numpy, matrix multiplication can be performed between non-square matrices as long as their inner dimensions align.
3. What is the output of this Python code?
Danke für Ihr Feedback!
Fragen Sie AI
Fragen Sie AI
Fragen Sie alles oder probieren Sie eine der vorgeschlagenen Fragen, um unser Gespräch zu beginnen
What happens if a matrix is not invertible in NumPy?
Can you explain more about the identity matrix?
How do you solve a system of equations using matrix inversion?
Awesome!
Completion rate improved to 1.89Matrix Operations in Python
Swipe um das Menü anzuzeigen
1. Matrix Operations: Addition and Subtraction
Two matrices A and B of the same shape can be added:
123456789import numpy as np A = np.array([[1, 2], [5, 6]]) B = np.array([[3, 4], [7, 8]]) C = A + B print(f'C = {C}') # C = [[4, 6], [12, 14]]
2. Matrix Multiplication Rules
Matrix multiplication is not element-wise.
Rule: if A has shape (n,m) and B has shape (m,l), then the result has shape (n,l).
123456789101112131415# Example random matrix 3x2 A = np.random.rand(3, 2) print(f'A = {A}') # Example random matrix 2x4 B = np.random.rand(2, 4) print(f'B = {B}') # product shape (3, 4) product = np.dot(A, B) print(f'np.dot(A, B) = {product}') # or equivalently product = A @ B print(f'A @ B = {product}')
3. Transpose
Transpose flips rows and columns.
General rule: if A is (n×m), then AT is (m×n).
12345A = np.array([[1, 2, 3], [4, 5, 6]]) A_T = A.T # Transpose of A print(A_T)
4. Inverse of a Matrix
A matrix A has an inverse A−1 if:
A⋅A−1=Iwhere I is the identity matrix.
Not all matrices have inverses. A matrix must be square and full-rank.
Quiz
- What does
np.linalg.inv(A)do in Python when solving the system $Ax = b$?
A) Rotates vector $x$ B) Eliminates matrix $A$ C) Reverses the linear transformation applied by $A$ D) None of the above
Correct Answer: C
Correct Answer: B
12345678A = np.array([[1, 2], [3, 4]]) A_inv = np.linalg.inv(A) # Inverse of A print(A_inv) I = np.eye(2) # Identity matrix 2x2 print(assert np.allclose(A @ A_inv, I)) # Check if product equals identity
1. What does the following Python code print?
2. In Python's numpy, matrix multiplication can be performed between non-square matrices as long as their inner dimensions align.
3. What is the output of this Python code?
Danke für Ihr Feedback!
