Skip to content

Commit

Permalink
Use upright font
Browse files Browse the repository at this point in the history
  • Loading branch information
@Tarang74
Tarang74 committed Jan 5, 2025
1 parent 1def961 commit 425b93d
Show file tree
Hide file tree
Showing 9 changed files with 46 additions and 46 deletions.
Binary file modified MXB106 Lecture Notes.pdf
View file
Binary file not shown.
Binary file modified figures/fundamental_subspaces.pdf
View file
Binary file not shown.
Binary file modified figures/matrix_transformation.pdf
View file
Binary file not shown.
Binary file modified figures/vector_position.pdf
View file
Binary file not shown.
Binary file modified figures/vector_projection.pdf
View file
Binary file not shown.
36 changes: 18 additions & 18 deletions tikz/fundamental_subspaces.tikz
View file
Original file line number Diff line number Diff line change
Expand Up @@ -43,32 +43,32 @@
% \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}{\(\dim{\left( \rowspace{A} \right)} = r\)}
}};
%
% Null Space
\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}{\(\dim{\left( \nullspace{A} \right)} = n - r\)}
}};
%
% Column Space
\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}{\(\dim{\left( \leftnullspace{A} \right)} = m - r\)}
}};
%
Expand All @@ -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
Expand All @@ -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}{\(r=\rank{\left( \symbf{A} \right)}=\rank{\left( \symbf{A}^\top \right)}\)}};
%
Expand Down
36 changes: 18 additions & 18 deletions tikz/matrix_transformation.tikz
View file
Original file line number Diff line number Diff line change
Expand Up @@ -48,32 +48,32 @@
% \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}{\(\dim{\left( \vcoim{\left( T \right)} \right)} = r\)}
}};
%
% Kernel
\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}{\(\dim{\left( \vker{\left( T \right)} \right)} = \dim{\left( V \right)} - r\)}
}};
%
% Image
\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}{\(\dim{\left( \vcoker{\left( T \right)} \right)} = \dim{\left( W \right)} - r\)}
}};
%
Expand All @@ -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}{\(r=\rank{\left( T \right)}\)}};
%
Expand Down
10 changes: 5 additions & 5 deletions tikz/vector_position.tikz
View file
Original file line number Diff line number Diff line change
Expand Up @@ -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}
\end{document}
10 changes: 5 additions & 5 deletions tikz/vector_projection.tikz
View file
Original file line number Diff line number Diff line change
Expand Up @@ -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}
Expand Down

0 comments on commit 425b93d

Please sign in to comment.