Linear Algebra Operations

Linear Algebra Operations in NumPy

NumPy provides a powerful module called numpy.linalg for linear algebra operations, which are essential in machine learning, physics, and engineering.

8. Matrix Creation

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# Creating two matrices
import numpy as np
 
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
 
print("Matrix A:\n", A)
print("Matrix B:\n", B)

Matrix Multiplication (Dot Product)

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# Matrix multiplication
dot_product = np.dot(A, B)
print("Dot Product:\n", dot_product)

Alternative:

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# You can also use the @ operator for matrix multiplication.
print("Dot Product using @ operator:\n", A @ B)

Matrix Transpose

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# Swaps rows and columns
print("Transpose of A:\n", A.T)

Determinant of a Matrix

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# Computing determinant
print("Determinant of A:", np.linalg.det(A))

Inverse of a Matrix

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# Computing inverse
print("Inverse of A:\n", np.linalg.inv(A))

Eigenvalues and Eigenvectors

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# Computing eigenvalues and eigenvectors
eigenvalues, eigenvectors = np.linalg.eig(A)
print("Eigenvalues:", eigenvalues)
print("Eigenvectors:\n", eigenvectors)

9. Why Linear Algebra is Important?

• Used in machine learning models, especially Principal Component Analysis (PCA).
• Essential for neural networks and deep learning.
• Helps in solving systems of linear equations.