Vectors

Question 1

What is a vector?

Answer 1

A data structure that represents a size and a magnitude, made up of at least 2 components.

Question 2

How can vectors be represented?

Answer 2

• List of numbers
• Functions
• Geometric point in space pointed to by an arrow

Question 3

How can a vector with n components from the set of reals be written?

Answer 3

Rⁿ

Question 4

How can a vector be represented using a dictionary?

Answer 4

• Key: The value in the domain
• Value: The image in the codomain

Question 5

How can we express a vector as a function?

Answer 5

f:S —> R where S is the set of values that the function can be applied to (domain) and R is the potential outputs of the function (co-domain)

Question 6

What is the dot product of 2 vectors?

Answer 6

The single value result when applying one vector’s magnitude and direction to another

Question 7

How do you calculate the dot product?
U = [u₁, u₂, … , u_n]
V = [v₁, v₂, … , v_n]

Answer 7

U x V = u₁v₁ + u₂v₂ + … u_nv_n

Question 8

What are the uses of the dot product?

Answer 8

Can be used to find the angle between them using the formula:
ab = |a||b|cosx

Question 9

What is a convex combination of two vectors?

Answer 9

A vector that lies on the line between two vectors

Question 10

When is D a convex combination where:
D = aA + bB
Where A, B are vectors and a,b are scalars

Answer 10

If a and b are both greater than or equal to 0 and a + b = 1