MODULE 01 · LESSON 03

Vectors

A vector is an ordered list. A matrix makes weighted sums from that list.

PLAIN-LANGUAGE INTRODUCTION

What is this?

A vector is an ordered list. A matrix makes weighted sums from that list.

One simple example

Use x = [2,3] and W = [[4,1],[1,2]]. Then Wx = [11,8].

A two-number vector and a matrix with two columns.

One weighted sum per matrix row. Here, the output is [11,8].

Neural layers use matrices to mix many input features at once.

A matrix does not know what its rows mean. Your program defines that meaning.

WORK THROUGH THE IDEA

A vector keeps numbers in order. Here, x₁ = 2 and x₂ = 3.
The first matrix row is [4,1]. Its weighted sum is 4×2 + 1×3 = 11.
The second row is [1,2]. Its weighted sum is 1×2 + 2×3 = 8.
The matrix has shape (2,2). The input has length 2. The output has length 2.
Common mistake: changing [2,3] to [3,2] changes the meaning and both weighted sums.