Why is Linear Algebra Useful?

Why is linear algebra actually useful? There very many applications of linear algebra. In data science, in particular, there are several ones of high importance. Some are easy to grasp, others not just yet. In this lesson, we will explore 3 of them:

• Vectorized code also known as array programming
• Image recognition
• Dimensionality reduction

Okay. Let’s start from the simplest and probably the most commonly used one – vectorized
code. We can certainly claim that the price of a house depends on its size. Suppose you know
that the exact relationship for some neighborhood is given by the equation:

Price equals 10,190 + 223 times size. Moreover, you know the sizes of 5 houses 693, 656, 1060, 487, and 1275 square feet.

What you want to do is plug-in each size in the equation and find the price of each house,
right?

Well, for the first one we get: 10190 + 223 times 693 equals 164,729. Then we can find the next one, and so on, until we find all prices.

Now, if we have 100 houses, doing that by hand would be quite tedious, wouldn’t it?

One way to deal with that problem is by creating a loop. You can iterate over the sizes, multiplying
each of them by 223, and adding 10,190. However, we are smarter than that, aren’t we? We know some linear algebra already. Let’s explore these two objects:

A 5 by 2 matrix and a vector of length 2. The matrix contains a column of 1s and another – with the sizes of the houses. The vector contains 10,190 and 223 – the numbers from the equation.
If we go about multiplying them, we will get a vector of length 5. The first element will be equal to:

1 times 10,190 plus 693 times 223. The second to:
1 times 10,190 plus 656 times 223. And so on.

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#LinearAlgebra #Math #DataScience

[theodenednew]

1. Vectorized Code
2. Image Recognition
3. Dimensionality Reduction

[MisouSup]

Amazing stuff! It's always important to have clear answers for "why do I need to study this"

[siddhantkohli]

I’m pursuing data science as my major n trust me linear algebra is v important if you want to be on top of the game👏🏽
Don’t take it leniently

[ucr]

As someone who has taken Linear Algebra in the past, I must admit Linear Algebra is a fun and worthwhile but challenging math class (especially if you are majoring in Computer Science and Mathematics). Yes, most of the calculations in Linear Algebra are simple, if you know the tricks and the concepts. But, what makes Linear Algebra a difficult math class is the proofs and they require abstract or critical thinking. If I had to rate the difficulty of this math class, I would say it is close to the difficulty level of Calculus 3 and Elementary Differential Equations. Plus, if someone were to pass Calculus 2 and is having trouble picking what math class to take next, I would recommend either taking Linear Algebra or Calculus 3 first, depending on your schedule, professor and school. Better yet, I would recommend taking these math classes concurrently because they go well together. Heck, Linear Algebra and Differential Equations also go well together. Bottom line, Linear Algebra is one of the best Math Classes that STEM majors will enjoy in college assuming if they pay attention and work hard at it.

[maxp]

I dropped out of an IT university years ago, because for months and months we were studying and solving dry higher math problems with the thought that "one day we will see how it's used in real life". I sucked at it, because I didn't like it and didn't understand the principles.

Teachers only gave vague answer to the question "Where will we use it?".
Being a visual learner, had they shown me a video like this, not only I'd be eager and excited to learn it, but also all of of the methods and principles would make sense.

[valeriisoldatov]

I like the way of explaining!
Really helps to understand the basics👍

[Saphir__]

"We know some linear algebra already don't we?"

Uh....no, no we do not.

[proterotype]

Thanks for the video. I’m prepping for a data science bootcamp and it helped to get me reacquainted with some of these concepts

[gursikh]

You did a good job. I Loved the way you explained the math skills used in data science.

[ducodarling]

Solves problem in two (not well written) lines of code
💡"But we're smarter than that!"
Makes a solution that requires a college class

This has been my overall experience when it comes to programming and higher maths. It seems like the math is there only to make the solution easier for humans to understand... but that's also the job of software tools, paradigms, and protocols. All programming is "array programming": numbers are arrays of bits, strings are arrays of numbers, and it's all stored in the memory array. How you organize that information in your head is irrelevant as far as computation is concerned. Likewise, how you organize the information in code is only as relevant as the compiler.

[logancarvalho]

This is great. Mainly because it explains the reasons behind a needed knowledge.
It's bad to just say: you need to know linear algebra ok?
Why? This video explains a lot. I'll look for further information about it. Thanks

[Mulkek]

Thanks, and it's so easy & simple!

[tylerandrews]

In the first example, what variable would the column of 1's represent if the others represent the size and the constants of the weighting vector? Could it be used to index a house id # or something similar? Or does it need to be all 1's? Great video!

[lnolyyq]

Really awesome, thank you for this clear explanation.

[guitarttimman]

Here's a challenge: Use visual basic to design a program that will sort records by the millions utilizing the random access function and combining it with matrices. I did that way back in the 80's with GW-Basic. At the time, all other programmers who tried it kept getting the OM (out of memory error). My program worked like a charm. The trouble is that the guy I designed it for ripped it, and now principles of the very same search routine were utilized to acceleration the processing speed in artificial intelligence. At the time I designed the program, I worked for Michael Tellerino in the City of Chicago. A.I., essentially, is what it is today because of me.

[GM-drdg]

I reject the premise re the first example re real estate. The first part of equation is likely off by a lot because no one wants to admit where there actual lines of value are in terms of where people put value. Zip codes are NOT proxies for real value.

[guitarttimman]

Great video, but a word of advice: Anything and everything you can learn about is useful.

[pianochannel]

I am not sure I agree with 'vectorized algorithms are faster'... In python yes, but in general probably not.

[bibhutibaibhavbora]

That's it tis is the video I was looking for.

[tolulopeojediran]

For someone without prior knowledge in Linear algebra. How does one know it?