Why is Linear Algebra Useful?
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- เผยแพร่เมื่อ 8 เม.ย. 2019
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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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This explanation is of high level. I expected you to explain it using examples of tickets or aeroplane following a line journey. Am I wrong?
Gud basic stuff
1. Vectorized Code
2. Image Recognition
3. Dimensionality Reduction
Amazing stuff! It's always important to have clear answers for "why do I need to study this"
Yes... Why shoul we learn messy stuff...? But now i get it..
Yes, must must
Exactly every messi topic or theory must first be known why to know it or study it where it will help!!
Elon musk told me the same thing
I like the way of explaining!
Really helps to understand the basics👍
Thanks for the video. I’m prepping for a data science bootcamp and it helped to get me reacquainted with some of these concepts
You did a good job. I Loved the way you explained the math skills used in data science.
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
Really awesome, thank you for this clear explanation.
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.
@Hugh Jones --- And Linear Algebra knowledge is required for Abstract Algebra, Number Theory and Partial Differential Equations.
Calc3 and Linear Algebra had minor over lap for me in the beginning, maybe the first two weeks. I would highly recommend that someone take Linear Algebra with Differential Equations or a Discrete Math class.
Linear algebra is next to nothing like calc 3... Calc 3 is way harder. Proofs in linear are so small and simple.. Discrete is when proofs get hard.
@@hayden3774 --- If we are talking about Calculus 3/Multivariable Calculus/Vector Calculus with an emphasis in Linear Algebra and proofs, then yes I would say that version of Calculus 3 is tougher than Linear Algebra. If we are talking about a less theoretical course in Calculus 3, then I would say the difficulty is on par with Linear Algebra (with the proofs and calculations) and Elementary Differential Equations (with less proofs and more calculations). Having said that, if someone were to pass Calculus 2, I would have them take Calculus 3 and/or Linear Algebra next and then deal with Differential Equations. I would also have them take discrete mathematics/proof writing (this prepares for upper division math classes like Abstract Algebra, Real Analysis, Number Theory, Differential Geometry, Partial Differential Equations, etc.). Note to self, my favorite but hardest math classes that I took in university were Linear Algebra, Multivariable Calculus and Differential Equations. I never got pass those math classes and switched to being an Economics major instead.
@@123ucr Yes calc 3 in CA is multivariable. I say linear is way easier because calc in general is pretty heavy on exponential equations and their graphs. Am a comp sci major dont need differentials unless I am going into computer engineering, at least in CA. My suggestion is calc 1-3, linear, then discrete.
Because multiplying matrices is very similar to dot product in calc 3, also it gives an easy break and a taste of doing proofs before discrete. Discrete is the hardest imo.
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.
Most people find it weird when I struggle with a subject if I don't know its real life applications and flourish when I do. It's very frustrating
Visual learning will only take you so far in math, that is why it's important to understand how theorems work. Similar reason why it's important to understand vector spaces.
great video, thanks!
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!
Thanks, and it's so easy & simple!
Glad you liked it!
"We know some linear algebra already don't we?"
Uh....no, no we do not.
thank you very much
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
You don't even need to learn it if you don't plan on doing anything with it
Great way thanks
Good explanation
Excellent.
That's it tis is the video I was looking for.
Great!
I wish it would longer
In physics vector is vector!
Amazing !!!!
pretty interesting!
I Love your videos
gotta love that z is a 3...
VERY NICE
9:40 Te
2:20 Isn't it plus 223 times 693?...
Brilliant
Neat.
Great video, but a word of advice: Anything and everything you can learn about is useful.
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.
So great of you
@@plumSlayer Thank you. As good as that was, it's nothing in comparison to what I could do with the right equipment.
I am not sure I agree with 'vectorized algorithms are faster'... In python yes, but in general probably not.
This looks like a typical Fortran program using Do loops.
Awesoem
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.
For someone without prior knowledge in Linear algebra. How does one know it?
Use Google
I'm learning it in school right now
@@NoMomICatntPause that is super interesting for everyone!
One learns it
If you make video games, you never have to ask if linear algebra is useful.
Data scientist.
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.
Can u provide me this full course in hindi.
whoah, theres nothing in the video!
quite good, thanks, but in RGB, B represents black not blue
RGB stands for Red Green Blue :)
Seriously?
Not deep explication, Thanks
Why am I a seventh grader watching this???
USing ladmarks is actually better for navigation because the brain dosnt operate in scientific units of measurement.
You can't spell algebra without bagel
why is linear algebra called linear algebra, rather than, say, digressive matrices, or patterned collections
Good start for those who refuse to take anything serious unless they can imagine a practical application.
People that are thus inclined probably should not study data science (or any math heavy subject).
I am so happy I never learned this.
It is more boring than watching the grass grow.
I chose this video because the thumbnail had a dog.
Hahaha
We understand 🐕
Good for you
Nah
Actually in 2024 I think they are called "photos of color"
Good explanation
Thanks so much!!