Agreed.Better than Netflix. How do I know? My wife was watching a movie,called me over and I sat next to her. Ten minutes into the movie and I was back to the lecture.
Im currently self studying pure maths and i wanted to say i love this series. I use two books for linear algebra, the gorge e shilov book and Axlers linear algebra done right and this series helps me get a grasp of fundamental concepts before i reach them in the books where the concepts are abstracted to the point where its hard to make sense of the concepts without a basic understanding. thank you
Great video. Though in the last example, the overall result is a 90-degree rotation. Is it not better to look at each action the matrix is taking, which are taking the inverse and then reflecting across the y-axis? (Or reflecting across x and then taking the inverse). Doesn't that help with visualizing the effects of different matrix operations?
Its been 3 months,but still if yiu are intrested to learn,you could email me on this comment email.I could teach you about on your doubts or confusion.Wait,For no cost ok,😅,don't worry.
Its getting flipped cause,she is not showing matrix calculation.First learn that matix operations.WHere you multiply whole row of T(x) by each column of u,in this case.
Yes, this is exaclty how rotations and translations are preformed by computers. If you want to rotate an image by say 90 degrees clockwise, you would multiply each vertex, which is represented by a vector, by the matrix that rotates the equation 90 degrees clockwise.
sorry if this is late, R2 pretty much just means you need 2 numbers to specify a location. For example, you'd need a number to denote an x, and another to denote y. in r3, you'll need 3 numbers to specify a location. one to denote an x (like x =4), one to denote a y (like y =3123), and another to denote a z (like z =12).
@@adrianhalvorsen7013 yes, R^1 is one dimension of real numbers (think of a number line that goes from negative infinity on the left all the way to positive infinity on the right), R^2 is two dimensions of real numbers (think of the x-y plane where the horizontal x-axis goes from negative infinity on the left to positive infinity on the right and the y-axis goes from negative infinity at the bottom to positive infinity at the top), and R^3 is three dimensions of real numbers (instead of just an x-axis and y-axis, you now have to add a z-axis that is perpendicular to the plane formed by the x-axis and y-axis). The capital letter "R" in blackboard bold font is used to represent "the set of all real numbers". Like yahoo pooper said, the 1, 2, or 3 lets you how many real numbers are needed to specify a location. (Once you get to R^4, R^5, R^6, and higher, it becomes impossible to visualize it in terms of geometry. It's better to just think of it as four, five, or six real numbers.)
They are all real comments. I’m sorry you flunked your exam, but you might try taking some personal responsibility for that. Read your textbook. Do your homework. Watch someone else’s videos if you don’t like mine.
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Woohoo! Unit 1 complete! Thanks again Professor B!
You bet!
Thank you Ms.Kimberly. If not for you, I would have been wandering in Linear Algebra. I like even your mistake too ;) much appreciated.
Glad it was helpful! I make many mistakes (though usually I edit them out)
Binge watching to this playlist. It's far better than any netflix show
Thank you for teaching us..
Agreed.Better than Netflix. How do I know? My wife was watching a movie,called me over and I sat next to her. Ten minutes into the movie and I was back to the lecture.
Im currently self studying pure maths and i wanted to say i love this series. I use two books for linear algebra, the gorge e shilov book and Axlers linear algebra done right and this series helps me get a grasp of fundamental concepts before i reach them in the books where the concepts are abstracted to the point where its hard to make sense of the concepts without a basic understanding. thank you
great tutorial. tks. in last example, the v is (2,3) but drawn on (2,2).
Thank you for letting me know!
So the two parallelograms have the same area, right?
Thanks prof.
Where is the more in-depth linear transformations video mentioned in this video?
chapter 4
Great video. Though in the last example, the overall result is a 90-degree rotation. Is it not better to look at each action the matrix is taking, which are taking the inverse and then reflecting across the y-axis? (Or reflecting across x and then taking the inverse). Doesn't that help with visualizing the effects of different matrix operations?
Kimberly, amazing lecture here. 💯 But please what text have you been referring to?
David Lay's Linear Algebra and It's Applications 5th
Excuse me may I ask why the numbers are getting flipped upside down at 6:37?
Its been 3 months,but still if yiu are intrested to learn,you could email me on this comment email.I could teach you about on your doubts or confusion.Wait,For no cost ok,😅,don't worry.
Its getting flipped cause,she is not showing matrix calculation.First learn that matix operations.WHere you multiply whole row of T(x) by each column of u,in this case.
Wait can’t a linear transformation add an offset to a vector? In that case wouldn’t transformation of zero vector not be zero?
Wow nice 👍👍
very useful!
In real world example, can we say that this the formula used in change image orientation/flipping in graphics? any thoughts
Not my area of expertise, but yes I believe you could use this type of method.
Yes, this is exaclty how rotations and translations are preformed by computers. If you want to rotate an image by say 90 degrees clockwise, you would multiply each vertex, which is represented by a vector, by the matrix that rotates the equation 90 degrees clockwise.
i love u
what i am struggling with is what does R2 mean? if you say it stays in R2? Is it number of dimensions?
sorry if this is late, R2 pretty much just means you need 2 numbers to specify a location. For example, you'd need a number to denote an x, and another to denote y. in r3, you'll need 3 numbers to specify a location. one to denote an x (like x =4), one to denote a y (like y =3123), and another to denote a z (like z =12).
@@yahoopooper9975 so it is dimensions?
@@adrianhalvorsen7013 yeah im p sure
@@adrianhalvorsen7013 yes, R^1 is one dimension of real numbers (think of a number line that goes from negative infinity on the left all the way to positive infinity on the right), R^2 is two dimensions of real numbers (think of the x-y plane where the horizontal x-axis goes from negative infinity on the left to positive infinity on the right and the y-axis goes from negative infinity at the bottom to positive infinity at the top), and R^3 is three dimensions of real numbers (instead of just an x-axis and y-axis, you now have to add a z-axis that is perpendicular to the plane formed by the x-axis and y-axis). The capital letter "R" in blackboard bold font is used to represent "the set of all real numbers". Like yahoo pooper said, the 1, 2, or 3 lets you how many real numbers are needed to specify a location. (Once you get to R^4, R^5, R^6, and higher, it becomes impossible to visualize it in terms of geometry. It's better to just think of it as four, five, or six real numbers.)
Complete
this is the only real comment probably thanks to you i got F in my exam
They are all real comments. I’m sorry you flunked your exam, but you might try taking some personal responsibility for that. Read your textbook. Do your homework. Watch someone else’s videos if you don’t like mine.
How is it HER fault YOU failed YOUR exam??😂
Clown bro she helped me get 95+ on all exams
Thanks for the laugh