Module 7: Linear Algebra with NumPy

Linear algebra is the mathematical engine behind Neural Networks and Machine Learning. NumPy provides the linalg module and dedicated operators to handle matrix math with extreme efficiency.

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Lesson 15: Linear Algebra Basics

Dot Product vs Element-wise Multiplication

• * (operator): Multiplies elements at the same position.
• @ (operator) or np.dot(): Performs standard Matrix Multiplication (Dot Product).

Transpose

Transposing flips a matrix over its diagonal, switching rows and columns.

• .T property: matrix.T

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Lesson 16: Advanced Linear Algebra

For more complex operations, we use np.linalg.

Key Functions:

• np.linalg.det(A): Calculates the Determinant of a matrix.
• np.linalg.inv(A): Calculates the Inverse (if it exists).
• np.linalg.eig(A): Returns Eigenvalues and Eigenvectors.

Solving Linear Equations

Imagine you have an equation: Ax = B. You can solve for x easily using np.linalg.solve(A, B).

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Practice: Matrix Inverse

Challenge: Create a random 3x3 matrix. Check if its determinant is non-zero. If it is, calculate its inverse. Then, multiply the original matrix by its inverse. What do you get? (Hint: It should be very close to the Identity Matrix).

Key Takeaways

✅ Use @ for Matrix Multiplication, not *.
✅ np.linalg contains solvers for equations, eigenvalues, and determinants.
✅ matrix.T is a quick way to transpose your data.