Linear algebra studies the dynamics of the simplest possible interactions among multiple variables. Its fundamentals are essential to all areas of mathematics.
Excellent description. Teaching mathematics is an art. Most lecturers fail by not explaining the nomenclature properly. They often assume students are familiar with complex notation. They often are not. Mathematics is a language like French or German - you need to learn the grammar and vocabulary to become proficient.
This is a great video! I have wanted to learn linear algebra for a few years now but have trouble staying motivated when I can't immediately apply the operations I'm learning to a real-world problem. Whenever I teach people to program I always start by teaching them how to make the computer move the mouse around, click on things, and type into the keyboard, because people can learn those few operations quickly and immediately use them to solve real problems.
Nathan Wailes I had the same problem - I recommend MIT/OCW's lectures by Prof. Gilbert Strang on youtube. Learning linear algebra takes patience as the appreciation doesn't come unless you understand some theory behind how various techniques are derived. If you need practical motivation, just keep in mind that all of engineering depends on linear algebra: building bridges/skyscrapers/planes, data compression, optimization problems (like how long to leave traffic light red or operations research), machine learning, statistics, physics, chemistry, etc... Watch Strang's lectures multiple times, if necessary, for the ideas to sink in. If ideas get too abstract, think of actual instances (like when you are solving an actual system of equations) to anchor yourself.
Thank you for this comment! I'm finding that I often have to be persistent in understanding the topics of Linear Algebra, watching and rewatching videos to reinforce my knowledge. Interestingly, I watched the "Big Picture of Linear Algebra" video by the professor you mentioned, Dr. Gilbert Strang, right before watching this video. As an additional recommendation, I really benefited from the "Essence of Linear Algebra" video series by the TH-cam user "3Blue1Brown". The graphics he produces and the insight he gives helps make many topics crystal-clear!
alkankondo89 If you haven't seen them already, 3Blue1Brown's series on Linear Algebra on TH-cam is the ABSOLUTE BEST I have seen for giving me a geometric intuition of why a determinant, null space/column space, rank, bases, eigenvalues/vectors, etc are useful. It's SO good that one can intuit geometrically why the column space and the null space are orthogonal (a kind of conservation of total number of input dimensions)! Unfortunately, he just touched on dual vectors without going deeper into dual spaces, etc... MathTheBeautiful, also on TH-cam, has lectures given by a professor, that goes slower (sometimes too slow) than MIT's Strang, but is more rigorous than 3Blue1Blue. This series is also worth viewing. Good luck!
I'm glad I stumbled upon this video--I think everyone should watch this before starting to learn Linear Algebra. I agree that it really is too abstract to begin with.
This is most helpful. Thank you for posting it. When at the end of the video you discuss using a matrix to perform operations from x_n to y_m, you seem to ignore the constant term(s). Some presenters exclude the constant term(s) altogether when discussing linear algebra. I'm not sure what to think about this. Does adding a constant term to each individual equation interfere with the use of matrices?
Good video but you need to balance your audio. The music is way too loud relative to the dialog. You probably already know this so hopefully any future Linear Algebra videos will have it resolved.
***** A multidimensional array in programming can be used to hold the entries of a matrix in linear algebra. However, the techniques and operations involved in linear algebra are exponentially more sophisticated. For example, in functional programming, you learn that data and functions are essentially the same. In linear algebra, you learn why: a matrix is simply a function which allows you to apply a linear transform to a vector. Chaining functions is equivalent to multiplying matrices together. The actual applications of linear algebra are also very broad. The most basic operation is solving a system of equations, but in the general case, this can even be applied to linear differential equations or any operators/functions which are closed under multiplication and addition. Later, you derive how least-squares best-fit line algorithms are solved in closed form. Even video/audio data compression is based on picking a good basis using linear algebra. A youtube comment cannot do the subject justice - but you will learn that almost all of engineering must use linear algebra in some way.
Amythest Gemini Before you even get into linear algebra you do need to know algebra. Linear algebra is simply algebra that uses matrices and more variables, but at the same time making algebra simpler. Also I really recommend you tackle linear algebra 1 before calculus 3, ODEs, and vector analysis, you will have a much simpler time with Multivariable calc.
Zzzip13Strike then it wouldnt be linear algebra. Linear algebra is the set of tools and techniques to solve systems of equations. Solving them via another method wouldnt be linear algebra.
why are matrices used in linear algebra. Why not any other data structure like a tree or graph?? I find in all books I've seen about Linear Algebra all use the same concept. Please help me I need to clear this doubt. I know matrix consists of same type of elements but still, couldn't I use any other data structure for the solving of linear equations ?
If you find a way to effectively reason with and manipulate vectors and vector spaces using a data structure other than a matrix, go for it and publish your results. Matrices are used because they allow us to reason about vectors and vector spaces in a useful way
Take pity on the fools who have "successfully" graduated from 12 years of being told to sit down/shut up/do what the teacher says. Few can concurrently master the punkrock/Do-It-Yourself attitude/values at the same time? If so, the whole "business" of college education/textbook revenues would collapse if kids were taught to use hyperphysics.edu.
trexinvert Pity the fool who only knows how to push buttons instead of actually working the problems out for himself. (O.K. fine! I'm 52 but that doesn't mean I'm over the hill yet!)
+mjh0123Six3 I'm right there with you, just 20 years younger. I like to numpy.linalg or defend myself in octave (free Matlab 'clone') as well but I like that it's not made up of black boxes and if one were to take that away from me, I'm just going to take a little longer.
Excellent description. Teaching mathematics is an art. Most lecturers fail by not explaining the nomenclature properly. They often assume students are familiar with complex notation. They often are not. Mathematics is a language like French or German - you need to learn the grammar and vocabulary to become proficient.
That intro was great man
I only subscribed to your channel because your intro was so fun!! I loved the video! Thank you for sharing! ☮
This is a great video! I have wanted to learn linear algebra for a few years now but have trouble staying motivated when I can't immediately apply the operations I'm learning to a real-world problem. Whenever I teach people to program I always start by teaching them how to make the computer move the mouse around, click on things, and type into the keyboard, because people can learn those few operations quickly and immediately use them to solve real problems.
Nathan Wailes I had the same problem - I recommend MIT/OCW's lectures by Prof. Gilbert Strang on youtube. Learning linear algebra takes patience as the appreciation doesn't come unless you understand some theory behind how various techniques are derived. If you need practical motivation, just keep in mind that all of engineering depends on linear algebra: building bridges/skyscrapers/planes, data compression, optimization problems (like how long to leave traffic light red or operations research), machine learning, statistics, physics, chemistry, etc... Watch Strang's lectures multiple times, if necessary, for the ideas to sink in. If ideas get too abstract, think of actual instances (like when you are solving an actual system of equations) to anchor yourself.
Thank you for this comment! I'm finding that I often have to be persistent in understanding the topics of Linear Algebra, watching and rewatching videos to reinforce my knowledge. Interestingly, I watched the "Big Picture of Linear Algebra" video by the professor you mentioned, Dr. Gilbert Strang, right before watching this video.
As an additional recommendation, I really benefited from the "Essence of Linear Algebra" video series by the TH-cam user "3Blue1Brown". The graphics he produces and the insight he gives helps make many topics crystal-clear!
alkankondo89 If you haven't seen them already, 3Blue1Brown's series on Linear Algebra on TH-cam is the ABSOLUTE BEST I have seen for giving me a geometric intuition of why a determinant, null space/column space, rank, bases, eigenvalues/vectors, etc are useful. It's SO good that one can intuit geometrically why the column space and the null space are orthogonal (a kind of conservation of total number of input dimensions)! Unfortunately, he just touched on dual vectors without going deeper into dual spaces, etc... MathTheBeautiful, also on TH-cam, has lectures given by a professor, that goes slower (sometimes too slow) than MIT's Strang, but is more rigorous than 3Blue1Blue. This series is also worth viewing. Good luck!
I'm glad I stumbled upon this video--I think everyone should watch this before starting to learn Linear Algebra. I agree that it really is too abstract to begin with.
Good job as an overview. Thank you.
love the way you explain so simply! thank you - great teacher!
i guess it's kinda randomly asking but do anyone know a good place to stream newly released tv shows online?
@Emery Arturo i watch on FlixZone. You can find it by googling :)
@Zachariah Troy Yup, I have been using FlixZone for since april myself :)
@Zachariah Troy thank you, I went there and it seems like they got a lot of movies there :D Appreciate it!
@Emery Arturo you are welcome :D
Excellent introductory overview.
Linear Algebra is the first course where you start seeing mathematical abstraction...then things become crazy
Lol....🤣 I couldn’t agree more David!
Thanks for this interesting introduction. Can you please share subsequent videos of the course also?
Thanks very good video.
Ohh, man!!!!
Your explanation is fantastic!!!
thank you. Finally all is clear
Great explanation!
Best video about the subject 👍💯🌴
Thank you. I was getting the exercises right. But I had no idea of what I was doing (or why). Now I know.
Thank you for clarity and depth together. There are no shortcuts to rigor.
There's a shortcut to rigor mortis.
This is most helpful. Thank you for posting it.
When at the end of the video you discuss using a matrix to perform operations from x_n to y_m, you seem to ignore the constant term(s).
Some presenters exclude the constant term(s) altogether when discussing linear algebra.
I'm not sure what to think about this.
Does adding a constant term to each individual equation interfere with the use of matrices?
I need that coffee grinder...
Thanks for creating this video!
that was really good, thank you!
Please try to make a full playlist of linear algebra
Good video but you need to balance your audio. The music is way too loud relative to the dialog. You probably already know this so hopefully any future Linear Algebra videos will have it resolved.
Holy moly. 30 second intro.. at the time of my viewing that's 66,000 views, which is 550 hours wasted on that intro.
Great intro vid! Why not go on and produce more awesome material
This is underrated !
This is most soporific branch of all mathematics.
which book is best for linear algebra?????
I is learnt'd something.
Is linear algebra similar to multidimensional arrays in programming in any way ?
***** A multidimensional array in programming can be used to hold the entries of a matrix in linear algebra. However, the techniques and operations involved in linear algebra are exponentially more sophisticated. For example, in functional programming, you learn that data and functions are essentially the same. In linear algebra, you learn why: a matrix is simply a function which allows you to apply a linear transform to a vector. Chaining functions is equivalent to multiplying matrices together. The actual applications of linear algebra are also very broad. The most basic operation is solving a system of equations, but in the general case, this can even be applied to linear differential equations or any operators/functions which are closed under multiplication and addition. Later, you derive how least-squares best-fit line algorithms are solved in closed form. Even video/audio data compression is based on picking a good basis using linear algebra. A youtube comment cannot do the subject justice - but you will learn that almost all of engineering must use linear algebra in some way.
neRD LOL
An addition is not a linear transformation. It sends the zero vector to a non zero vector.
That is a clarificaton needed. The linear function in calculus is not a linear transformation, but an affine one
sick intro bro
Chevere
un saludo a todos los colombianos!
what’s the reason for the list at 1:30?
I'd it important I learn algebra 1 and 2 first before leaving liner algebra? I'm using khan academy and just need some guidance.
Amythest Gemini
Take a crash course in all of them, then get in depth.
Amythest Gemini Before you even get into linear algebra you do need to know algebra. Linear algebra is simply algebra that uses matrices and more variables, but at the same time making algebra simpler. Also I really recommend you tackle linear algebra 1 before calculus 3, ODEs, and vector analysis, you will have a much simpler time with Multivariable calc.
Nice explanation
Yes algebra 1 geometry algebra 2
Foreplay can be short , for sure.........
So Linear Algebra is good for ... being the tangent line for more complicated functions...
Great video, but the music in the start is annoying
A random and disjoint sequence of thought.
Does linear algebra without matrices exist?
does the english alphabet without the letter a exist?
Mario Mirdita Yeah, if you write everything out in regular equations or maybe even just sentences
Zzzip13Strike then it wouldnt be linear algebra. Linear algebra is the set of tools and techniques to solve systems of equations. Solving them via another method wouldnt be linear algebra.
That cheesy intro, but good video :D
Is there any use of linear algebra at age 50?
No. Once you turn 50, linear algebra becomes useless.
He packs a lot of ideas into one short video.
"Topics in a Linear Algebra Course"
mathworld.wolfram.com/classroom/classes/LinearAlgebra.html
More about what LA is, rather than what the title proposes, why?
i'm brazilian and i watch your channel.
Kayllon Duarte
A Brazilian learning math?! A miracle
Se bem que o Brasil é um dos tops na matemática, em uma visão mundial.
why are matrices used in linear algebra. Why not any other data structure like a tree or graph?? I find in all books I've seen about Linear Algebra all use the same concept. Please help me I need to clear this doubt. I know matrix consists of same type of elements but still, couldn't I use any other data structure for the solving of linear equations
?
If you find a way to effectively reason with and manipulate vectors and vector spaces using a data structure other than a matrix, go for it and publish your results. Matrices are used because they allow us to reason about vectors and vector spaces in a useful way
*** Hippie Alert***
Skip to 0:33
is he a freshman?
Not a fan of the intro.
I am a fan of the intro.
@@abid5330 who?
The music at first is too loud and irritating
Wedtaena.Wedtara.Wedteafal.
This is more calculus than linear
this guy is like a worse version of math antics
Wtf is with that intro. Jesus!
thx bro
Jesus is the Son of God
he loves you
Believe in him and repent
What an awful awful intro. No need for an intro??
+Austin Schrader Yeah now that my ears are blown out lets learn some linear algebra...
BYPASS INTRO >>>>>> 0:32
Needed for beginners.
Feedback: The intro is too long and unpleasant.
Why Linear Algebra folderol?
Because the undergraduate fools don’t know that linear algebra software is readily available on the internet.
Take pity on the fools who have "successfully" graduated from 12 years of being told to sit down/shut up/do what the teacher says. Few can concurrently master the punkrock/Do-It-Yourself attitude/values at the same time? If so, the whole "business" of college education/textbook revenues would collapse if kids were taught to use hyperphysics.edu.
trexinvert Pity the fool who only knows how to push buttons instead of actually working the problems out for himself. (O.K. fine! I'm 52 but that doesn't mean I'm over the hill yet!)
+mjh0123Six3 I'm right there with you, just 20 years younger.
I like to numpy.linalg or defend myself in octave (free Matlab 'clone') as well but I like that it's not made up of black boxes and if one were to take that away from me, I'm just going to take a little longer.