Matrix Multiplication
Matrix Multiplication is the dot product between each number.
1, 2, 3 2, 4, 6 Pos1, Pos2, Pos3
4, 5, 6 x 3, 6, 9 = Pos4, Pos5, Pos6
7, 8, 9 4, 8, 12 Pos7, Pos8, Pos9
Pos 1 = 1×2 + 2×4 + 3×6 = 2 + 8 + 18 = 28
Pos 2 = 2×2 + 2×4 + 2×6 = 4 + 8 + 12 = 24
Pos 3 = 3×2 + 3×4 + 3×6 = 6 + 12 + 18 = 36
Pos 4 = 4×3 + 4×6 + 4×9 = 12 + 24 + 36 = 72
Pos 5 = 5×3 + 5×6 + 5×9 = 15 + 30 + 45 = 90
Pos 6 = 6×3 + 6×6 + 6×9 = 18 + 36 + 54 = 108
Pos 7 = 7×4 + 7×8 + 7×12 = 28 + 56 + 84 = 168
Pos 8 = 8×4 + 8×8 + 8×12 = 32 + 64 + 96 = 192
Pos 9 = 9×4 + 9×8+ 9×12 = 36 + 72 + 108 = 226
28, 24, 36
72, 90, 108
168, 192, 226
Dot Products
Dot product is the cosine of the angle between 2 vectors, multiplied by the magnitude of each vector.
Cosine is the ratio of the side adjacent to an angle and the longest side (hypotenuse) in a right angled triangle.
Dot product is calculated by multiplying together the corresponding component from the 2 vectors and adding up the results.
(1,2) . (3,4)
1 x 3 = 3
2 x 4 = 8
3+8 = 11
________________
(-3, 6) . (2,3)
-3 x 2 = -6
6 x 3 = 18
-6 + 18 = 12
________________
(-1.5,4) . (-4, -0.8)
-1.5 x -4 = -6
4 x -0.8 = -3.2
-6 + -3.2 = -9.2
(2,4,6) . (-0.5, 0.5, -0.5)
2 x -0.5 = -1
4 x 0.5 = 2
6 x -0.5 = -3
-1 + 2 + -3 = -2
Cross Products
The result of a cross product is a new vector at 90 degrees.
Cross Products are a series of multiplications with 2 vectors.
(1,2,3,) – (4,5,6)
X Y Z
| 1 | 2 | 3 | 1 | 2 | 3 |
| 4 | 5 | 6 | 4 | 5 | 6 |
X = 2 x 6 – 3 x 5 = 12 – 15 = -3 Y = 3 x 4 – 1 x 6 = 12 – 6 = 6 Z = 1 x 5 – 2 x 4 = 5 – 8 = -3
(-3, 6, -3)
Averages (Mode, Median, Range, Mean)
Median refers to middle number in arranged order
if there is no middle, then the middle value of the 2 most middle numbers
Mode is the most common occurrence in a set of data
Range is the largest number minus the lowest number
Mean is all the numbers added together and divided by total numbers in sequence.
Remembering Pythag
SOH-CAH-TOA – The angle can be found in the following ways
Sine = Opposite / Hypotenuese
Cosine = Adjacent / Hypotenuese
Tangent = Opposite / Adjacent
Hypotenuse relates to the angle between the opposite and adjacent. The adjacent is the horizontal base of the triangle and the opposite is the vertical height of the triangle.
JORDAN | GLITCH ARCADE 