Linear Algebra

Question 1

Where does the word ‘vector’ come from?

Answer 1

The Latin for ‘carrier’, from a vectors propensity to move something from one location to another.

Question 2

In some traditional courses, how are vectors often represented?

Answer 2

As a list of number, e.g. [1, 3.14, -2, 0]

Question 3

A vector with 4 entries, each of which is a real number, is called what?

Answer 3

A 4-vector over ℝ. Denoted ℝ⁴

Question 4

What must all entries in a vector have in common?

Answer 4

They must all be drawn from the same field, e.g. ℂ, ℝ, or GF(2), etc…

Question 5

The set of n-vectors over ℝ is denoted how?

Answer 5

ℝⁿ

Question 6

How can you think of the 4-vector [3.14159, 2.71828, 0, -1] in terms of function mapping?

Answer 6

0 ↦ 3.14159, 1 ↦ 2.71828, 2 ↦ 0, 3 ↦ -1}. Or in Python { 0: 3.14159, 1: 2.71828, 2: 0, 3: 1}.

Question 7

Write the notation to indicate that ƒ is a function that maps from WORDS to ℝ

Answer 7

ƒ:WORDS→ℝ

Question 8

For a finite set i and a field F, a function from i to F is called what?

Answer 8

An i-vector over F, denote Fⁱ