Vectors, Matrices, and Convolutions

Prof. Dr. Alessandro Del Vecchio · 7 concepts · 5 questions

Concept 1 / 7

Vectors — A List of Numbers

A vector is a 1D np.ndarray — the simplest multi-element data structure in NumPy. The same concept appears across radically different domains:

Domain	Vector contents	Example shape
Tabular data (one patient)	`(age, height, weight, BMI)`	`(4,)`
Image pixel (colour)	`(R, G, B)`	`(3,)`
LLM embedding	1536 semantic dimensions	`(1536,)`
EMG feature	`(RMS, ARV, mean_freq)` per window	`(3,)`

NumPy is natively vectorised — all basic operations work element-wise without Python loops:

import numpy as np
u = np.array([1.0, 2.0, 3.0])
v = np.array([4.0, 5.0, 6.0])

print(u + v)       # [5. 7. 9.]  — element-wise addition
print(2.5 * u)     # [2.5 5.  7.5]  — scalar scaling

Writing explicit Python for loops over NumPy arrays is almost always slower and unnecessary — embrace vectorised operations.