Foundations

Vectors, span, linear transformations, matrix multiplication, determinants. The goal is geometric intuition - you should see a matrix as a transformation of space.

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Exercises

• In NumPy, implement matrix-vector multiplication by hand (no @), then verify against np.matmul.
• Write a function that rotates 2D points by an angle theta using a rotation matrix; plot a shape before and after.
• Compose two transformations (rotate then shear) and show the composed matrix equals the product.

Checkpoint

Explain, out loud, why matrix multiplication is not commutative - using pictures, not algebra.

Finish the linear algebra series (dot products, cross products, change of basis, eigenvectors). Then the two extras your quantum future depends on: complex numbers and unitary/hermitian matrices. Close with derivatives and gradients for training neural nets.

Study

• Essence of Linear Algebra, chapters 9-16 (same playlist as Week 1).
• Mathematics for Machine Learning (free book): skim ch. 2-4 as reinforcement; read section 5.1-5.5 on gradients properly.
• Complex numbers refresher: any source you like; you need e^(i*theta), magnitude, conjugate, and why |z|^2 = z * conj(z).

Exercises

• Compute eigenvalues/eigenvectors of a 2x2 matrix by hand, verify with np.linalg.eig, and plot the eigenvector directions before/after the transformation.
• Show numerically that a 2x2 rotation matrix is unitary (its conjugate transpose is its inverse).
• Implement numerical gradient checking for f(x, y) = x^2 y + sin(y) and compare with the analytic gradient.

Checkpoint

You can state what makes a matrix unitary and why that will matter for quantum gates (they preserve vector length - probability).

Vectorized thinking. The difference between someone who can use PyTorch and someone who fights it is NumPy broadcasting.

Study

• CS231n Python/NumPy tutorial - do every snippet, do not copy-paste.
• NumPy broadcasting rules - read the official docs page and predict outputs before running.

Exercises

• Implement k-nearest-neighbors from scratch (no loops over samples - vectorize the distance matrix) on a toy 2-class dataset; plot the decision boundary.
• Implement standardization, one-hot encoding, and a train/validation/test split as reusable functions in your lab repo.
• Speed check: time the looped vs vectorized distance computation on 10,000 points and record the ratio in your notes.

Checkpoint

Given shapes (32, 1, 8) and (8,), you can predict the broadcast result shape without running it.

The domain layer. Radio signals arrive as complex I/Q samples; every model you build later eats these. This week you learn what they are and how to make them.

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Study

• PySDR (free book) - chapters on I/Q sampling, the frequency domain, and digital modulation. This is your DSP spine; it is written for exactly this course's purpose.

Exercises

• Generate a BPSK and a QPSK signal in NumPy from random bits; plot the constellation diagrams.
• Add white Gaussian noise at several SNRs; watch the constellations smear. Write a reusable add_awgn(signal, snr_db) function - Capstone A will use it.
• Compute and plot the FFT and a spectrogram of your QPSK signal with scipy.signal.spectrogram.
• Optional hardware: with an RTL-SDR dongle, capture live FM radio and plot its spectrum. Nothing makes I/Q data feel real faster.

Checkpoint

You can explain to a friend what the I and Q in I/Q stand for, and why complex numbers show up in radio at all.