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??
- As a map
- As a function
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??
- Addition
- Multiplication
- Dot product
- Convex combination
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Metadata
date: 2020-11-09 14:27
tags:
- '@?computing'
- '@?public'
- '@?fundementals-of-data-structures'
title: Computing - Vectors