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

What are the values of a and b below, given that matrix A=
$\begin{bmatrix}
1 & 2 & 9\\
a & 5 & 2\\
b & 2 & 1
\end{bmatrix}$ is symmetric?


What are the values of a and b below, given that matrix A=
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>9</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>5</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><annotation encoding="application/x-tex">\begin{bmatrix}
1 &amp; 2 &amp; 9\\
a &amp; 5 &amp; 2\\
b &amp; 2 &amp; 1
\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>⎡​1ab​252​921​⎦<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>⎤​ is symmetric?


$\begin{bmatrix}6\\ 2\\ 13\end{bmatrix}$


$\begin{bmatrix}1&1&1\\ 0&2&0\\ 0&6&9\end{bmatrix}$

What’s the result of the following matrix-vector multiplication? 

$\begin{bmatrix}1&1&1\\ 0&1&0\\ 0&2&3\end{bmatrix}\begin{bmatrix}1\\ 2\\ 3\end{bmatrix}=?$

What’s the result of the following matrix-vector multiplication?
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</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></mtable><mo fence="true">]</mo></mrow><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"><mn>2</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>3</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mo stretchy="false">?</mo></mrow><annotation encoding="application/x-tex">\begin{bmatrix}1&amp;1&amp;1\\ 0&amp;1&amp;0\\ 0&amp;2&amp;3\end{bmatrix}\begin{bmatrix}1\\ 2\\ 3\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>⎡​100​112​103​⎦<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>⎤​⎣<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>⎡​123​⎦<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>⎤​=?


Multiplying a matrix of order $m\times n$ with another matrix of order $n \times p$ gives us a resultant matrix of order $m \times p$.

Matrix multiplication can sometimes be commutative.


Every linear combination is also a convex combination.

(**True** or **false**.) Every diagonal matrix is also a lower and an upper triangular matrix.

(True or false.) Every diagonal matrix is also a lower and an upper triangular matrix.

$\begin{bmatrix}w_1 \\ w_2\end{bmatrix}$


$\begin{bmatrix} 2 & 3 \\ 1 & 9 \end{bmatrix}
$

$\begin{bmatrix} 2 & 3 & 5\\ 1 & 9 & 1 \end{bmatrix}$

Which matrix can’t be created from the following linear system?

$2w_1 + 3w_2 = 5$,

$w_1+  9w_2 = 0$



Which matrix can’t be created from the following linear system?
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><msub><mi>w</mi><mn>1</mn></msub><mo>+</mo><mn>3</mn><msub><mi>w</mi><mn>2</mn></msub><mo>=</mo><mn>5</mn></mrow><annotation encoding="application/x-tex">2w_1 + 3w_2 = 5</annotation></semantics></math>2w1​+3w2​=5,
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>w</mi><mn>1</mn></msub><mo>+</mo><mn>9</mn><msub><mi>w</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">w_1+ 9w_2 = 0</annotation></semantics></math>w1​+9w2​=0

Multiple-choice questions

Multiple-choice questions

Test your knowledge of matrices 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: Matrices and Matrix Operations