vectors

Question 1

what is a vector

Answer 1

A vector is a mapping from a set of indices to real values.

Question 2

list notation
set notation

Answer 2

[2.0, 3.14159, -1.0, 2.718281828] - This is called a 4-vector because it has 4 elements.

A 4-vector over ℝ (the set of real numbers) is written as: ℝ⁴

Question 3

Function Interpretation of a Vector

Answer 3

For vector [2.0, 3.14159, -1.0, 2.718281828], it can be seen as:

0 ↦ 2.0
1 ↦ 3.14159
2 ↦ -1.0
3 ↦ 2.718281828

Question 4

what does the dot product tell us

Answer 4

If result is 0, vectors are perpendicular.

If result > 0, angle is acute.

If result < 0, angle is obtuse.