Tidy up

docs/lectures/graphics/03_graphic_math.md

@@ -3,14 +3,14 @@
 ### Vectors
 
 - The n-dimensional Euclidean Space is $\mathbb{R}^n$
-  - $\mathbb{R}^n = \{(v_0, v_1, ... v_{n-1}) | v_0, v_1, ...v_{n-1} \in \mathbb{R}\}$ 
-- A vector is an n-turple
+    - $\mathbb{R}^n = \{(v_0, v_1, ... v_{n-1}) | v_0, v_1, ...v_{n-1} \in \mathbb{R}\}$
+- A vector is an n-tuple
 - $v\in \mathbb{R}^n \Longleftrightarrow v=(v_0, v_1, ...v_{n-1}) | v_0, v_1, ...v_{n-1} \in \mathbb{R}$
 - In computer graphics we normally deal with 3-Dimensional Euclidean space $\mathbb{R}^3$
-  - vec3 notation:
-    - $v=(v_0, v_1, v_2)$
-    - $v = \begin{pmatrix} {v_0}\\{v_1}\\{v_2} \end{pmatrix}$
-  - Where $v_0$ represents x, $v_1$ represents y, and $v_2$ represents z axis
+    - vec3 notation:
+        - $v=(v_0, v_1, v_2)$
+        - $v = \begin{pmatrix} {v_0}\\{v_1}\\{v_2} \end{pmatrix}$
+    - Where $v_0$ represents the x axis, $v_1$ represents the y axis, and $v_2$ represents the z axis
 
 ##### Vector Scaling
 
@@ -104,18 +104,18 @@ Two matrices can only be multiplied if they both have the same number of columns
 
 To get the resulting matrix, for each $(x,y)$ pair, is the cross product of the $x^{th}$ column and the $y^{th}$ row.
 
-- Matrix multiplication is not communative
-  - $MN \neq NM$
+- Matrix multiplication is not commutative
+    - $MN \neq NM$
 
 ###### Matrix-Vector Multiplication
 
-A matrix multiplied by vector gives new vector
+A matrix multiplied by a vector gives a new vector
 
 Each row of the resulting vector is that row of the vector, dot producted with that row on the matrix.
 
 ##### Trigonometry
 
-If $p=(p_x, p_y)$ is a unit vector, we can write them as:
+If $p=(p_x, p_y)$ is a unit vector, we can write its components as:
 
 $$
 p_x = cos \space \alpha \\