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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

## Statement
Write a `largestIndependentSubsetCalculator` function that takes a collection of vectors $S = \{v_1, v_2, \cdots, v_n\}$, where all vectors belong to the same vector space, and returns the largest linearly independent subset (this subset could be any subset and need not be unique).

## Example
Consider an example of a collection of vectors:

$$\{(1, 4, 7),(2, 5, 8),(3, 6, 9)\}$$

The largest possible independent subset of the collection is $\{(1, 4, 7),(2, 5, 8)\}$

## Sample inputs and outputs
The following table describes the desired outputs of the corresponding inputs (including a few that are taken from the set of vectors above).
|  Input | Output  |
| :----: | :----: |
| $S:[[1, 4, 7],[2, 5, 8],[3, 6, 9]]$| $[[1, 4, 7],[2, 5, 8]]$   |
| $S:[[7, 52, 58],[90, 76, 36],[67, 90, 13]]$ | $[[7, 52, 58],[90, 76, 36],[67, 90, 13]]$ |
| $S:[[5, 3, 2],[6, 7, 8],[5, 3, 2],[1, 4, 6]]$ | $[[5, 3, 2],[6, 7, 8]]$ |


## Try it yourself
The signature of a function is given below. It accepts an array 
of vectors and returns an array of linearly independent vectors.

# Statement
Write a `largestIndependentSubsetCalculator` function that takes a collection of vectors $S = \{v_1, v_2, \cdots, v_n\}$, where all vectors belong to the same vector space, and returns the largest linearly independent subset (this subset could be any subset and need not be unique).

# Example
Consider an example of a collection of vectors:

$$\{(1, 4, 7),(2, 5, 8),(3, 6, 9)\}$$

The largest possible independent subset of the collection is $\{(1, 4, 7),(2, 5, 8)\}$

# Sample inputs and outputs
The following table describes the desired outputs of the corresponding inputs (including a few that are taken from the set of vectors above).
|  Input | Output  |
| :----: | :----: |
| $S:[[1, 4, 7],[2, 5, 8],[3, 6, 9]]$| $[[1, 4, 7],[2, 5, 8]]$   |
| $S:[[7, 52, 58],[90, 76, 36],[67, 90, 13]]$ | $[[7, 52, 58],[90, 76, 36],[67, 90, 13]]$ |
| $S:[[5, 3, 2],[6, 7, 8],[5, 3, 2],[1, 4, 6]]$ | $[[5, 3, 2],[6, 7, 8]]$ |


# Try it yourself
The signature of a function is given below. It accepts an array 
of vectors and returns an array of linearly independent vectors.

Program a Python algorithm to find the linearly independent subset of a collection of vectors.

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

Challenge: Calculate the Largest Independent Subset

Statement

Example

Sample inputs and outputs

Try it yourself

Input	Output
$S:[[1, 4, 7],[2, 5, 8],[3, 6, 9]]$	$[[1, 4, 7],[2, 5, 8]]$
$S:[[7, 52, 58],[90, 76, 36],[67, 90, 13]]$	$[[7, 52, 58],[90, 76, 36],[67, 90, 13]]$
$S:[[5, 3, 2],[6, 7, 8],[5, 3, 2],[1, 4, 6]]$	$[[5, 3, 2],[6, 7, 8]]$