Intermediate·24 min·0/47 done

NumPy arrays and vectors

Create arrays, check shape and dtype, then compute cosine similarity.

Why it matters: Embeddings are vectors. Batches are matrices. Similarity search is a dot product of normalized vectors.

Basics

Arrays, shape, and dtype

A NumPy array is a typed block of numbers. Operations run over the whole array at once.

Check these first when debugging:

shape - sizes of each axis, e.g. (32, 768)
dtype - usually float32 in ML code

Common mistake: mixing dtypes and silently doubling memory.

Tiny example

Make a small vector and print shape and dtype.

import numpy as np
a = np.array([0.1, 0.9, 0.3], dtype=np.float32)
print(a.shape, a.dtype)

Basics

Vectorization and broadcasting

Vectorization means writing a * 2 + b instead of a Python loop.

Broadcasting lets arrays of compatible shapes combine. A (768,) mean can subtract from a (32, 768) batch.

Shapes must match from the right: equal size, or one side is 1.

Tiny example

Subtract the column mean from a tiny batch.

import numpy as np
batch = np.array([[1.0, 2.0], [3.0, 4.0]])
print(batch - batch.mean(axis=0))

Basics

Cosine similarity

Cosine similarity is the dot product of two unit vectors.

Normalize each vector (divide by its L2 norm), then multiply with @.

Values near 1 mean similar direction. This is the core of vector search.

Tiny example

Normalize two vectors, then take the dot product.

import numpy as np
a = np.array([1.0, 0.0])
b = np.array([0.8, 0.2])
a_n = a / np.linalg.norm(a)
b_n = b / np.linalg.norm(b)
print(float(a_n @ b_n))

Then AI / ML

AI / ML examples

Same idea, used in real AI work. Press Try in lab to run it.

AI / ML example

AI / ML: center a batch of embeddings

One broadcast subtracts the mean from every row.

In AI / ML: Embedding batches are matrices; mean vectors broadcast across rows.

example.py

Python

import numpy as np

embeddings = np.array([[1.0, 2.0, 3.0], [2.0, 4.0, 6.0]], dtype=np.float32)
mean_vec = embeddings.mean(axis=0)
centered = embeddings - mean_vec
print(mean_vec)
print(centered)

AI / ML example 2

AI / ML: rank docs by cosine score

Normalize, then score a query against a small doc matrix.

In AI / ML: Semantic search ranks documents by cosine similarity to a query vector.

example.py

Python

import numpy as np

def normalize(m):
    norms = np.linalg.norm(m, axis=1, keepdims=True)
    return m / np.clip(norms, 1e-9, None)

docs = np.array([[0.9, 0.1], [0.1, 0.9], [0.8, 0.2]], dtype=np.float32)
labels = ["python", "k8s", "tools"]
query = np.array([[0.85, 0.15]], dtype=np.float32)
scores = (normalize(query) @ normalize(docs).T)[0]
for i in np.argsort(-scores):
    print(labels[i], round(float(scores[i]), 3))

Takeaways

1Check .shape and .dtype first when debugging arrays.
2Prefer vectorized ops; broadcasting applies a small array across a large one.
3Cosine similarity on normalized vectors powers semantic search.

Certificate