Computing - Vectors | Olly Britton

What is a vector an example of?

An Abstract Data Type

What set do all $2$-d vectors come from?

\[\mathbb{R}^2\]

What set do all $3$-d vectors come from?

\[\mathbb{R}^3\]

What’s an example of where a $2$-d vector could be used?

To describe a path.

What does the notation $S \to \mathbb{R}$ mean?

$S$ maps to $\mathbb{R}$.

What is the notation $0 \to 1.5$ mean in terms of vectors?

$0$ maps to $1.5$.

What is the most common representation for a vector?

A list.

What would be the python code to represent the vector $[1, 2]$?

vec = [1,2]

How could you view a vector as a function?

It takes sequential input values like $0,1,2,3$ and converts them into other values like $-1.3, 3.4, 5.8, 4.2$.

Other than a list, how could you represent a vector?

What is the convex combination of two vectors?

The space bounded by the triangle formed by joining the vectors with a line.

If you have two vectors $u$ and $v$, how could you describe their conex combination?

\[w = \alpha u + \beta v\] \[\text{where} \quad \alpha, \beta >= 0 \quad \text{and} \quad \alpha + \beta = 1\]

What is the dot product of two vectors?

The value formed by multipling all the matching elements of a vector and adding them.

How can you think of the dot product of two vectors?

The multiplication of a single row and a single column matrix.

What does $u \cdot v$?

The dot product of $u$ and $v$.

What are the 4 operations on a vector at A-level?