diff --git a/MXB106 Lecture Notes.pdf b/MXB106 Lecture Notes.pdf
index bd1778a..dd7e759 100644
Binary files a/MXB106 Lecture Notes.pdf and b/MXB106 Lecture Notes.pdf differ
diff --git a/figures/fundamental_subspaces.pdf b/figures/fundamental_subspaces.pdf
index 8606592..d0ffb89 100644
Binary files a/figures/fundamental_subspaces.pdf and b/figures/fundamental_subspaces.pdf differ
diff --git a/figures/matrix_transformation.pdf b/figures/matrix_transformation.pdf
index 7ef0d96..324bd13 100644
Binary files a/figures/matrix_transformation.pdf and b/figures/matrix_transformation.pdf differ
diff --git a/figures/vector_position.pdf b/figures/vector_position.pdf
index e70988a..c0ff679 100644
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diff --git a/figures/vector_projection.pdf b/figures/vector_projection.pdf
index 1a0e126..c21ff54 100644
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diff --git a/tikz/fundamental_subspaces.tikz b/tikz/fundamental_subspaces.tikz
index c89869b..8488b96 100644
--- a/tikz/fundamental_subspaces.tikz
+++ b/tikz/fundamental_subspaces.tikz
@@ -43,9 +43,9 @@
 	% \draw[<->, thick] (10,0) -- (0,0) -- (0,10);
 	% Row Space
 	\filldraw \shapeProperties \rotateOne (\pivotOneX, \pivotOneY) rectangle (\pivotOneX + 5, \pivotOneY + 4.1);
-	\node at \rotateXY{\pivotOneX + 5 / 2}{\pivotOneY + 4.1 / 2}{\pivotOneX}{\pivotOneY}{\angleOne} 
+	\node at \rotateXY{\pivotOneX + 5 / 2}{\pivotOneY + 4.1 / 2}{\pivotOneX}{\pivotOneY}{\angleOne}
 	{\shortstack{
-		\scalebox{2}{\(\rowspace{A}\)} \\ 
+		\scalebox{2}{\(\rowspace{A}\)} \\
 		\scalebox{1.5}{\(\dim{\left( \rowspace{A} \right)} = r\)}
 	}};
 	%
@@ -53,7 +53,7 @@
 	\filldraw \shapeProperties \rotateOne (\pivotOneX - 5.3, \pivotOneY - 6) rectangle (\pivotOneX, \pivotOneY);
 	\node at \rotateXY{\pivotOneX - 5.3 / 2}{\pivotOneY - 6 / 2}{\pivotOneX}{\pivotOneY}{\angleOne}
 	{\shortstack{
-		\scalebox{2}{\(\nullspace{A}\)} \\ 
+		\scalebox{2}{\(\nullspace{A}\)} \\
 		\scalebox{1.5}{\(\dim{\left( \nullspace{A} \right)} = n - r\)}
 	}};
 	%
@@ -61,14 +61,14 @@
 	\filldraw \shapeProperties \rotateTwo (\pivotTwoX, \pivotTwoY) rectangle (\pivotTwoX + 4.4, \pivotTwoY + 5.3);
 	\node at \rotateXY{\pivotTwoX + 4.4 / 2}{\pivotTwoY + 5.3 / 2}{\pivotTwoX}{\pivotTwoY}{\angleTwo}
 	{\shortstack{
-		\scalebox{2}{\(\columnspace{A}\)} \\ 
+		\scalebox{2}{\(\columnspace{A}\)} \\
 		\scalebox{1.5}{\(\dim{\left( \columnspace{A} \right)} = r\)}
 	}};
 	% Left Null Space
 	\filldraw \shapeProperties \rotateTwo (\pivotTwoX - 6.9, \pivotTwoY - 3.9) rectangle (\pivotTwoX, \pivotTwoY);
 	\node at \rotateXY{\pivotTwoX - 6.9 / 2}{\pivotTwoY - 3.9 / 2}{\pivotTwoX}{\pivotTwoY}{\angleTwo}
 	{\shortstack{
-		\scalebox{2}{\(\leftnullspace{A}\)} \\ 
+		\scalebox{2}{\(\leftnullspace{A}\)} \\
 		\scalebox{1.5}{\(\dim{\left( \leftnullspace{A} \right)} = m - r\)}
 	}};
 	%
@@ -82,30 +82,30 @@
 	%
 	% Zeros
 	\draw [fill] (\pivotOneX, \pivotOneY) circle [radius=0.05];
-	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(\symbfup{0}\)}}}] at (\pivotOneX, \pivotOneY) {};
+	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(\symbf{0}\)}}}] at (\pivotOneX, \pivotOneY) {};
 	\draw [fill] (\pivotTwoX, \pivotTwoY) circle [radius=0.05];
-	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(\symbfup{0}\)}}}] at (\pivotTwoX, \pivotTwoY) {};
+	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(\symbf{0}\)}}}] at (\pivotTwoX, \pivotTwoY) {};
 	%
 	% Homogeneous vector
 	\draw [fill] \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} circle [radius=0.05];
-	\node[label={[label distance=0.25]180:{\scalebox{1.25}{\(\symbfit{x}_h\)}}}] at     \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} {};
+	\node[label={[label distance=0.25]180:{\scalebox{1.25}{\(\symbf{x}_h\)}}}] at     \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} {};
 	% Particular vector
 	\draw [fill] \rotateXY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne} circle [radius=0.05];
-	\node[label={[label distance=0.25]180:{\scalebox{1.25}{\(\symbfit{x}_p\)}}}] at     \rotateXY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne} {};
+	\node[label={[label distance=0.25]180:{\scalebox{1.25}{\(\symbf{x}_p\)}}}] at     \rotateXY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne} {};
 	% b vector
 	\draw [fill] \rotateXY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} circle [radius=0.05];
-	\node[label={[label distance=0.25]0:{\scalebox{1.25}{\(\symbfit{b}\)}}}] at \rotateXY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} {};
+	\node[label={[label distance=0.25]0:{\scalebox{1.25}{\(\symbf{b}\)}}}] at \rotateXY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} {};
 	% General vector
 	\draw [fill] (-1, 1.3) circle [radius=0.05];
-	\node[label={[label distance=0.25]325:{\scalebox{1.25}{\(\symbfit{x}=\symbfit{x}_p+\symbfit{x}_h\)}}}][below right] at (-1, 1.3) {};
+	\node[label={[label distance=0.25]325:{\scalebox{1.25}{\(\symbf{x}=\symbf{x}_p+\symbf{x}_h\)}}}][below right] at (-1, 1.3) {};
 	%
-	% Homogeneous Equation 
+	% Homogeneous Equation
 	\draw [thick] \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} -- (\pivotTwoX, \pivotTwoY);
 	\draw [->, thick] \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} -- ({(\pivotTwoX + \rotateX{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\pivotTwoY + \rotateY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2});
-	% Particular Equation 
+	% Particular Equation
 	\draw [thick] \rotateXY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne} -- \rotateXY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo};
 	\draw [->, thick] \rotateXY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne} -- ({(\rotateX{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateX{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\rotateY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2});
-	% General Equation 
+	% General Equation
 	\draw [thick] (-1, 1.3) -- \rotateXY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo};
 	\draw [->, thick] (-1, 1.3) -- ({(-1 + \rotateX{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo}) / 2}, {(1.3 + \rotateY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo}) / 2});
 	% Dotted Particular Vector
@@ -114,12 +114,12 @@
 	\draw [dashed] \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} -- (-1, 1.3);
 	%
 	% Particular Equation Label
-	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(\symbf{A}\symbfit{x}_p=\symbfit{b}\)}}}] at ({(\rotateX{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateX{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\rotateY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}) {};
+	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(\symbf{A}\symbf{x}_p=\symbf{b}\)}}}] at ({(\rotateX{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateX{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\rotateY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}) {};
 	% General Equation Label
-	\node[label={[label distance=0.25]325:{\scalebox{1.25}{\(\symbf{A}\symbfit{x}=\symbfit{b}\)}}}] at ({(-1 + \rotateX{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo}) / 2}, {(1.3 + \rotateY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo}) / 2}) {};
+	\node[label={[label distance=0.25]325:{\scalebox{1.25}{\(\symbf{A}\symbf{x}=\symbf{b}\)}}}] at ({(-1 + \rotateX{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo}) / 2}, {(1.3 + \rotateY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo}) / 2}) {};
 	% Homogeneous Equation Label
-	\node[label={[label distance=0.25]325:{\scalebox{1.25}{\(\symbf{A}\symbfit{x}_h=\symbfup{0}\)}}}] at ({(\pivotTwoX + \rotateX{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\pivotTwoY + \rotateY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}) {};
-	% 
+	\node[label={[label distance=0.25]325:{\scalebox{1.25}{\(\symbf{A}\symbf{x}_h=\symbf{0}\)}}}] at ({(\pivotTwoX + \rotateX{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\pivotTwoY + \rotateY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}) {};
+	%
 	% Rank definition
 	\node at (0,6.5) {\scalebox{1.75}{\(r=\rank{\left( \symbf{A} \right)}=\rank{\left( \symbf{A}^\top \right)}\)}};
 	%
diff --git a/tikz/matrix_transformation.tikz b/tikz/matrix_transformation.tikz
index ee787c6..f4fef69 100644
--- a/tikz/matrix_transformation.tikz
+++ b/tikz/matrix_transformation.tikz
@@ -48,9 +48,9 @@
 	% \draw[<->, thick] (10,0) -- (0,0) -- (0,10);
 	% CoImage
 	\filldraw \shapeProperties \rotateOne (\pivotOneX, \pivotOneY) rectangle (\pivotOneX + 5, \pivotOneY + 4.1);
-	\node at \rotateXY{\pivotOneX + 5 / 2}{\pivotOneY + 4.1 / 2}{\pivotOneX}{\pivotOneY}{\angleOne} 
+	\node at \rotateXY{\pivotOneX + 5 / 2}{\pivotOneY + 4.1 / 2}{\pivotOneX}{\pivotOneY}{\angleOne}
 	{\shortstack{
-		\scalebox{2}{\(\vcoim{\left( T \right)}\)} \\ 
+		\scalebox{2}{\(\vcoim{\left( T \right)}\)} \\
 		\scalebox{1.5}{\(\dim{\left( \vcoim{\left( T \right)} \right)} = r\)}
 	}};
 	%
@@ -58,7 +58,7 @@
 	\filldraw \shapeProperties \rotateOne (\pivotOneX - 5.3, \pivotOneY - 6) rectangle (\pivotOneX, \pivotOneY);
 	\node at \rotateXY{\pivotOneX - 5.3 / 2}{\pivotOneY - 6 / 2}{\pivotOneX}{\pivotOneY}{\angleOne}
 	{\shortstack{
-		\scalebox{2}{\(\vker{\left( T \right)}\)} \\ 
+		\scalebox{2}{\(\vker{\left( T \right)}\)} \\
 		\scalebox{1.5}{\(\dim{\left( \vker{\left( T \right)} \right)} = \dim{\left( V \right)} - r\)}
 	}};
 	%
@@ -66,14 +66,14 @@
 	\filldraw \shapeProperties \rotateTwo (\pivotTwoX, \pivotTwoY) rectangle (\pivotTwoX + 4.4, \pivotTwoY + 5.3);
 	\node at \rotateXY{\pivotTwoX + 4.4 / 2}{\pivotTwoY + 5.3 / 2}{\pivotTwoX}{\pivotTwoY}{\angleTwo}
 	{\shortstack{
-		\scalebox{2}{\(\vim{\left( T \right)}\)} \\ 
+		\scalebox{2}{\(\vim{\left( T \right)}\)} \\
 		\scalebox{1.5}{\(\dim{\left( \vim{\left( T \right)} \right)} = r\)}
 	}};
 	% CoKernel
 	\filldraw \shapeProperties \rotateTwo (\pivotTwoX - 6.9, \pivotTwoY - 3.9) rectangle (\pivotTwoX, \pivotTwoY);
 	\node at \rotateXY{\pivotTwoX - 6.9 / 2}{\pivotTwoY - 3.9 / 2}{\pivotTwoX}{\pivotTwoY}{\angleTwo}
 	{\shortstack{
-		\scalebox{2}{\(\vcoker{\left( T \right)}\)} \\ 
+		\scalebox{2}{\(\vcoker{\left( T \right)}\)} \\
 		\scalebox{1.5}{\(\dim{\left( \vcoker{\left( T \right)} \right)} = \dim{\left( W \right)} - r\)}
 	}};
 	%
@@ -84,40 +84,40 @@
 	% Number set
 	\node[label={[label distance=40]180:{\scalebox{3}{\(V\)}}}] at (\pivotOneX,\pivotOneY) {};
 	\node[label={[label distance=40]0:{\scalebox{3}{\(W\)}}}] at (\pivotTwoX,\pivotTwoY) {};
-	% 
+	%
 	% Zeros
 	\draw [fill] (\pivotOneX, \pivotOneY) circle [radius=0.05];
-	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(\symbfup{0}\)}}}] at (\pivotOneX, \pivotOneY) {};
+	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(\symbf{0}\)}}}] at (\pivotOneX, \pivotOneY) {};
 	\draw [fill] (\pivotTwoX, \pivotTwoY) circle [radius=0.05];
-	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(\symbfup{0}\)}}}] at (\pivotTwoX, \pivotTwoY) {};
+	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(\symbf{0}\)}}}] at (\pivotTwoX, \pivotTwoY) {};
 	%
 	% Kernel
 	\draw [fill] \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} circle [radius=0.05];
-	\node[label={[label distance=0.25]180:{\scalebox{1.25}{\(\symbfit{v}\)}}}] at \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} {};
+	\node[label={[label distance=0.25]180:{\scalebox{1.25}{\(\symbf{v}\)}}}] at \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} {};
 	% Vector
 	\draw [fill] \rotateXY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne} circle [radius=0.05];
-	\node[label={[label distance=0.25]180:{\scalebox{1.25}{\(\symbfit{v}\)}}}] at \rotateXY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne} {};
+	\node[label={[label distance=0.25]180:{\scalebox{1.25}{\(\symbf{v}\)}}}] at \rotateXY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne} {};
 	% Transformed vector
 	\draw [fill] \rotateXY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} circle [radius=0.05];
-	\node[label={[label distance=0.25]0:{\scalebox{1.25}{\(T\left(\symbfit{v}\right)\)}}}] at \rotateXY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} {};
+	\node[label={[label distance=0.25]0:{\scalebox{1.25}{\(T\left(\symbf{v}\right)\)}}}] at \rotateXY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} {};
 	%
-	% Kernel Equation 
+	% Kernel Equation
 	\draw [thick] \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} -- (\pivotTwoX, \pivotTwoY);
 	\draw [->, thick] \rotateXY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne} -- ({(\pivotTwoX + \rotateX{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\pivotTwoY + \rotateY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2});
-	% Transformation Equation 
+	% Transformation Equation
 	\draw [thick] \rotateXY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne} -- \rotateXY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo};
 	\draw [->, thick] \rotateXY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne} -- ({(\rotateX{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateX{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\rotateY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2});
-	% Transformation of 0 Equation 
+	% Transformation of 0 Equation
 	\draw [thick] (\pivotOneX , \pivotOneY) -- (\pivotTwoX, \pivotTwoY);
 	\draw [->, thick] (\pivotOneX , \pivotOneY) -- ({(\pivotOneX + \pivotTwoX) / 2}, {(\pivotOneY + \pivotTwoY) / 2});
 	%
 	% Transformation Equation Label
-	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(T\left(\symbfit{v}\right)=\symbf{A}\symbfit{v}\)}}}] at ({(\rotateX{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateX{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\rotateY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}) {};
+	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(T\left(\symbf{v}\right)=\symbf{A}\symbf{v}\)}}}] at ({(\rotateX{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateX{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\rotateY{\pivotTwoX + 0.9}{\pivotTwoY + 1.7}{\pivotTwoX}{\pivotTwoY}{\angleTwo} + \rotateY{\pivotOneX + 1.3}{\pivotOneY + 1.1}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}) {};
 	% Transformation of 0 Equation Label
-	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(T\left(\symbfup{0}\right)=\symbfup{0}\)}}}] at ({(\pivotOneX + \pivotTwoX) / 2}, {(\pivotOneY + \pivotTwoY) / 2}) {};
+	\node[label={[label distance=0.25]90:{\scalebox{1.25}{\(T\left(\symbf{0}\right)=\symbf{0}\)}}}] at ({(\pivotOneX + \pivotTwoX) / 2}, {(\pivotOneY + \pivotTwoY) / 2}) {};
 	% Kernel Equation Label
-	\node[label={[label distance=0.25]325:{\scalebox{1.25}{\(T\left(\symbfit{v}\right)=\symbfup{0}\)}}}] at ({(\pivotTwoX + \rotateX{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\pivotTwoY + \rotateY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}) {};
-	% 
+	\node[label={[label distance=0.25]325:{\scalebox{1.25}{\(T\left(\symbf{v}\right)=\symbf{0}\)}}}] at ({(\pivotTwoX + \rotateX{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}, {(\pivotTwoY + \rotateY{\pivotOneX - 1.8}{\pivotOneY - 1.5}{\pivotOneX}{\pivotOneY}{\angleOne}) / 2}) {};
+	%
 	% Rank definition
 	\node at (0,6.5) {\scalebox{1.75}{\(r=\rank{\left( T \right)}\)}};
 	%
diff --git a/tikz/vector_position.tikz b/tikz/vector_position.tikz
index 5cdfda4..7f98f85 100644
--- a/tikz/vector_position.tikz
+++ b/tikz/vector_position.tikz
@@ -15,16 +15,16 @@
 \begin{tikzpicture}
 	\draw [<->] (0,5) -- (0,0) -- (5,0); % Axes
 	% First Vector
-	\draw [->, dashed, opacity=0.65] (0,0) -- (1,4); 
+	\draw [->, dashed, opacity=0.65] (0,0) -- (1,4);
 	\node [right] at (0.5,2) {\(\overrightarrow{OA}\)};
-	\node [above left] at (1,4) {\(\symbfit{a}\)};
+	\node [above left] at (1,4) {\(\symbf{a}\)};
 	% Second Vector
 	\draw [->, dashed, opacity=0.65] (0,0) -- (4,2);
 	\node [below right] at (2,1) {\(\overrightarrow{OB}\)};
-	\node [below right] at (4,2) {\(\symbfit{b}\)};
+	\node [below right] at (4,2) {\(\symbf{b}\)};
 	% Displacement Vector
 	\draw [->, thick] (1,4) -- (4,2);
-	\node [above right] at (2.5,3) {\(\overrightarrow{AB} = \symbfit{b} - \symbfit{a}\)};
+	\node [above right] at (2.5,3) {\(\overrightarrow{AB} = \symbf{b} - \symbf{a}\)};
 	\node [below left] at (0,0) {\(O\)};
 \end{tikzpicture}
-\end{document}
\ No newline at end of file
+\end{document}
diff --git a/tikz/vector_projection.tikz b/tikz/vector_projection.tikz
index 3946540..05b5fa2 100644
--- a/tikz/vector_projection.tikz
+++ b/tikz/vector_projection.tikz
@@ -20,17 +20,17 @@
 \begin{tikzpicture}
 	\draw [<->] (0,5) -- (0,0) -- (5,0); % Axes
 	% a
-	\draw [->, thin, opacity=0.65] (0,0) -- (4.5,3.9); 
-	\node [below right] at (4.5,3.9) {\(\symbfit{a}\)};
+	\draw [->, thin, opacity=0.65] (0,0) -- (4.5,3.9);
+	\node [below right] at (4.5,3.9) {\(\symbf{a}\)};
 	% b
 	\draw [->, thick] (0,0) -- (0.8,4);
-	\node [left] at (0.7,4) {\(\symbfit{b}\)};
+	\node [left] at (0.7,4) {\(\symbf{b}\)};
 	% p
 	\draw [->, thick] (0,0) -- (2.43655,2.11168);
-	\node [right] at ({2.43655 / 2 + 0.25},{2.11168/2}) {\(\symbfit{p}=\proj_{\symbfit{a}}\symbfit{b}=\symbfit{a}x\)};
+	\node [right] at ({2.43655 / 2 + 0.25},{2.11168/2}) {\(\symbf{p}=\proj_{\symbf{a}}\symbf{b}=\symbf{a}x\)};
 	% e
 	\draw [->, thick, dashed, opacity=0.65] (2.43655,2.11168) -- (0.8,4);
-	\node [above right] at (1.61827,3.05584) {\(\symbfit{e}=\symbfit{b}-\symbfit{p}\)};
+	\node [above right] at (1.61827,3.05584) {\(\symbf{e}=\symbf{b}-\symbf{p}\)};
 	% Right angle
 	\draw[-, very thin] (2.27282,2.3006) -- (2.08389,2.13686) -- (2.24763,1.94794);
 \end{tikzpicture}