linear algebra week2 the modulus

Modulus & inner product

coordinate system(4) = 4

vector(24) = 24
length(11) = 11
direction(6)
define(10) = 10
1.what mean by a vector, the mathematical propery of vector(length and direction)
2.define commutative, distributive, associative over scalar multiplication

property(9) = 9
Pythagoras(3) = 3
square(9) = 9
component(10) = 10

dimension(7) = 7
unit vector
a,b = 2

multiply(10) = 10
dot product(12) = 12
size

commutative(5) = 5
distributive (3) = 3
associative over scalar multiplication(2) = 2

Cosine & dot product

cosine(3) = 3
square(15) = 15
angle(7) = 7

vector(11) = 11
dot product(8) = 8

根据余弦定理，推断出dot product = 2 |r| |s| cosx
orthogonal(2) = 2 (dot product = zero)

Projection

vector(21) = 21
projection(20) = 20

dot product = |r|*projection(s to r)

angle(+ triangle) = 7
hypotenuse(3 + 2 right-handed) = 5

shadow(5) = 5
two explanations of projection(s above, r below, s onto r):
1.s cosx
2.r.s / |r|

scalar projection / vector projection(unit vector * scalar projection)
vector projection = dot product / r.r * r