Gain insights into linear algebra essentials for data science, focusing on vectors, matrices, and tensors. Explore practical Python applications, engaging visuals, real datasets, and hands-on projects.

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Linear algebra is a fundamental pillar of data science. In advanced models in data science, like neural networks, the inputs and transformations are based upon vectors, matrices, and tensors which require a reasonable understanding of linear algebra to get the desired results. It is elegant and the most applied mathematics under the umbrella of data science.

This course teaches linear algebra with a focus on data science. This course encompasses several engaging illustrations, including static images and animations. Furthermore, this course presents mathematical modeling through programming in Python. This course contains several executable coding playgrounds on real data sets and a final project with practical applications.

Aside from theoretical implementations, the modern-day world needs its daunting calculations, trajectory mapping, and distance manipulation, all of which linear algebra provides. By the end of this course, you’ll have a working knowledge of all the necessary teachings in linear algebra.

Linear Algebra for Data Science Using Python

$\alpha_1=\frac{1}{2},\alpha_2=\frac{1}{2}$

For what values of $\alpha_1$ and $\alpha_2$, $\begin{bmatrix}
3 \\
5  \\
9 
\end{bmatrix}=\alpha_1\begin{bmatrix}
3 \\
5  \\
9 
\end{bmatrix}+\alpha_2\begin{bmatrix}
3 \\
5  \\
9 
\end{bmatrix}$  

For what values of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>α</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">\alpha_1</annotation></semantics></math>α1​ and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>α</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\alpha_2</annotation></semantics></math>α2​, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>3</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>5</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>9</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><msub><mi>α</mi><mn>1</mn></msub><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>3</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>5</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>9</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>+</mo><msub><mi>α</mi><mn>2</mn></msub><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>3</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>5</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>9</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix}
3 \\
5 \\
9 
\end{bmatrix}=\alpha_1\begin{bmatrix}
3 \\
5 \\
9 
\end{bmatrix}+\alpha_2\begin{bmatrix}
3 \\
5 \\
9 
\end{bmatrix}</annotation></semantics></math>⎣<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M319 0 H403 V16 H319z M319 0 H403 V16 H319z'/></svg>⎡​359​⎦<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M263 0 H347 V16 H263z M263 0 H347 V16 H263z'/></svg>⎤​=α1​⎣<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M319 0 H403 V16 H319z M319 0 H403 V16 H319z'/></svg>⎡​359​⎦<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M263 0 H347 V16 H263z M263 0 H347 V16 H263z'/></svg>⎤​+α2​⎣<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M319 0 H403 V16 H319z M319 0 H403 V16 H319z'/></svg>⎡​359​⎦<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M263 0 H347 V16 H263z M263 0 H347 V16 H263z'/></svg>⎤​

For what values of $a$ and $b$, $\begin{bmatrix}
-1 \\
2 \\
4 
\end{bmatrix}=2\begin{bmatrix}
1 \\
a  \\
2 
\end{bmatrix}-3\begin{bmatrix}
2 \\
5  \\
b 
\end{bmatrix}$  

For what values of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math>a and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi></mrow><annotation encoding="application/x-tex">b</annotation></semantics></math>b, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mn>1</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>4</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mn>2</mn><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>−</mo><mn>3</mn><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>5</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix}
-1 \\
2 \\
4 
\end{bmatrix}=2\begin{bmatrix}
1 \\
a \\
2 
\end{bmatrix}-3\begin{bmatrix}
2 \\
5 \\
b 
\end{bmatrix}</annotation></semantics></math>⎣<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M319 0 H403 V16 H319z M319 0 H403 V16 H319z'/></svg>⎡​−124​⎦<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M263 0 H347 V16 H263z M263 0 H347 V16 H263z'/></svg>⎤​=2⎣<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M319 0 H403 V16 H319z M319 0 H403 V16 H319z'/></svg>⎡​1a2​⎦<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M263 0 H347 V16 H263z M263 0 H347 V16 H263z'/></svg>⎤​−3⎣<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M319 0 H403 V16 H319z M319 0 H403 V16 H319z'/></svg>⎡​25b​⎦<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M263 0 H347 V16 H263z M263 0 H347 V16 H263z'/></svg>⎤​

$\begin{bmatrix}
-1 & 4 & 0\\
2 & 2 & 3\\
4 & -1 & 7
\end{bmatrix}$

$\begin{bmatrix}
3 & 5 & 0\\
2 & 8 & 3\\
0 & -1 & 4
\end{bmatrix}$

$\begin{bmatrix}
1 & 4 & 0\\
2 & 2 & 3\\
4 & -1 & 7
\end{bmatrix}$

$\begin{bmatrix}
0 & 0 & 0\\
0 & 0 & 0\\
0 & 0 & 0
\end{bmatrix}$

Given $X=\begin{bmatrix}
-1 & 4 & 0\\
2 & 2 & 3\\
4 & -1 & 7
\end{bmatrix}$ and $Y=\begin{bmatrix}
3 & 5 & 0\\
2 & 8 & 3\\
0 & -1 & 4
\end{bmatrix}$, which combination of $X$ and $Y$ isn't linear?

Given <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mn>1</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>4</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>3</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>4</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mn>1</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>7</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">X=\begin{bmatrix}
-1 &amp; 4 &amp; 0\\
2 &amp; 2 &amp; 3\\
4 &amp; -1 &amp; 7
\end{bmatrix}</annotation></semantics></math>X=⎣<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M319 0 H403 V16 H319z M319 0 H403 V16 H319z'/></svg>⎡​−124​42−1​037​⎦<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M263 0 H347 V16 H263z M263 0 H347 V16 H263z'/></svg>⎤​ and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>3</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>5</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>8</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>3</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mn>1</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>4</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">Y=\begin{bmatrix}
3 &amp; 5 &amp; 0\\
2 &amp; 8 &amp; 3\\
0 &amp; -1 &amp; 4
\end{bmatrix}</annotation></semantics></math>Y=⎣<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M319 0 H403 V16 H319z M319 0 H403 V16 H319z'/></svg>⎡​320​58−1​034​⎦<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='0.016em' style='width:0.6667em' viewBox='0 0 666.67 16' preserveAspectRatio='xMinYMin'><path d='M263 0 H347 V16 H263z M263 0 H347 V16 H263z'/></svg>⎤​, which combination of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math>X and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y</annotation></semantics></math>Y isn’t linear?

Multiple-choice questions

Multiple-choice questions

Test your knowledge of linear functions and linear combinations by completing this quiz.

Introduction

Linearity

Matrices

Solving Linear Systems

Singularity

Linear Regression and Least Squares

Vector Space

Vector Spaces of a Matrix

Singular Value Decomposition: SVD

Learning to Find Discriminative Null Space for Face Recognition

Quiz: Linear Functions and Combinations