4.2.8 Vectors

What can vectors be represented as?

• A list of numbers

• A vector space over a field

• A function

• Point in space

How may a vector be written as a list of numbers?

[2.5, 3.5, 4.5]

How may a vector be represented as a space over a field?

A 2-vector over R —> R²

How may a vector be represented as a function?

f: S → R where S is the set {0, 1, 2] and R the set of real numbers

0 → 2.5

1 → 3.5

2 → 4.5

How can vectors be implemented in a program?

• Array

• List

• Dictionary

How are vectors added?

[x1, y1] + [x2, y2] = [(x1+x2), (y2+y2)]

What is the effect of adding vectors?

Translation

How are vectors multiplied?

[x1, y1] * [x2, y2] = [(x1*x2), (y2*y2)]

What is the effect of multiplying vectors?

Scaling up/down

What is the convex combination of two vectors?

αu + βv

→ α+β = 1

→ α, β ≥ 0

What is meant by finding the dot product of two vectors?

Multiplying

How can the angle between two vectors be found?

• Calculate dot product

• Calculate magnitudes of u and v

• Calculate the product of u and v magnitudes

• Calculate cos0

• Find cosine inverse