I love these wee videos, your inspiring words got me through my 1st and 2nd year engineering maths courses! Thanks so much and keep up the good work 🧙♂️ Ps 1st!
A good way I remember how to find the matrix is to see what vectors the linear transformations turns the canonical basis vectors, e1 hat, e2 hat and e3 hat, etc into. The resulting vectors are the columns of your matrix.
So you are basically saying , given a linear mapping (transformation) T: x --> y , where x is in R^n and y is in R^m, then the transformation T can also be expressed by the matrix equation T(x) = A . x , where A is an m x n matrix defined by A = [ T( e_1) , T(e_2) , ... T(e_n) ] , and e_i are the canonical basis vectors in R^n. Note that the vector x in R^n should be treated as an n x 1 matrix so that the matrix multiplication A . x is valid, and the output T(x) is an m x 1 matrix.
Little note this is a matrix of given transformation with respect to standard basis. What really confuses me is when we have to compute matrix with respect to non standard basis
unfortunately in terms of polynomials this method doesn't work properly (if sb figured out why, please reply my comment), its' output is 90 degrees flipped matrix. Correct way is to write (x1, x2, x3) as matrix ([1,0,0], [0,1,0], [0,0,1]) then do the operation as for 4:46: (1/2, 0, 1) (1, 1, 1) (1, -1, 1/4) and now these vectors write in columns, so: [1/2, 1, 1] [0, 1, -1] [1, 1, 1/4]
In the first example we get 3 equations from 2 variables so it's increased dimensions But in the 2nd example we get 3 variables and turn it into 3 equations so the dimension doesn't change
Can you do the question to find the matrix with the respect of standard basis of R^2 and R^3 please ? I could not understand what I need to do with standard basis ! Thanks
@cjjk9142 but dim V = dim W , I think it's necessary not sufficient condition for a map to be surjective. If a map is surjective then obviously both domain and co-domain must have same dimension but I don't think it's inverse is always true. For a map to be surjective the condition was ImT = W.
Trigonometry hardly comes up in linear algebra 1, you need to understand the cosine function for angles between vectors and you need to understand the sine function as well for rotation matrices but it's all rather basic trigonometry. In terms of algebra, I assume you mean the manipulation of equations and not algebra concerning group theory etcetera. Yes understanding basic algebra is important but you don't need to "master" it. That being said linear algebra is a new algebra with all kinds of different rules which are very interesting and useful tools for later in your math career. It was one of my favourite courses so far.
I would say if you can understand the derivation of a rotation matrix you probably know enough trig. There is a good video about it from Khan Academy and I’m sure from other places. That was the most trig I saw used in linear algebra other than being familiar with sine and cosine for the scalar product and cross product. Although that is more of a calc 3 thing.
@@gustopher6500 how much basic algebra do I need please? Only the rules and properties of functions and graphs and linear equations? Because in a lot of books like the one by Hoffman and Kunze and the other one by Anton they do make a small review. Thanks
@@gustopher6500 and what is the best linear algebra book in your opinion for computer science and math that has good explanations and good exercises and examples? Thanks in advance
I love how u didnt skip a SINGLE STEP. thank u
Exactly what I want to understand. Like how we can represent a function or mapping or transformation in form of Matrix. Thanks a lot 🙏🏻
Many thanks for this I have been searching online and wasting 2 hours for nothing until I have seen your video well done please keep up
You have provided a clear solution. It is so wise and kind of you to help me with my studies!
are you student ?
I love these wee videos, your inspiring words got me through my 1st and 2nd year engineering maths courses! Thanks so much and keep up the good work 🧙♂️
Ps 1st!
11 months later, it's still useful to someone in de world. Thanks 🙏🏿
A good way I remember how to find the matrix is to see what vectors the linear transformations turns the canonical basis vectors, e1 hat, e2 hat and e3 hat, etc into. The resulting vectors are the columns of your matrix.
So you are basically saying , given a linear mapping (transformation) T: x --> y , where x is in R^n and y is in R^m,
then the transformation T can also be expressed by the matrix equation T(x) = A . x ,
where A is an m x n matrix defined by A = [ T( e_1) , T(e_2) , ... T(e_n) ] , and
e_i are the canonical basis vectors in R^n.
Note that the vector x in R^n should be treated as an n x 1 matrix so that the
matrix multiplication A . x is valid, and the output T(x) is an m x 1 matrix.
@jacobharris5894 thanks great comment screenshotted this lol
Thanks very much!!! you made it really easier to understand than my lecturer's explanation 🙇♀️
👍👍
Thank you for your time and effort to teach this.
Thank you! Very easy to understand! I definitely needed this!!!!!!
I am so glad this video helped someone! Thank you for this comment! Maybe I should make more of these it's been a while since I've made these.
@@TheMathSorcerer I think you have the best video on this topic
Thanks a lot sir .
Your videos have been so helpful to me.🙏🙏lots of love and support from India 🇮🇳 ❤️
thank you! i didnt realize how easy it was until you showed us !!
Little note this is a matrix of given transformation with respect to standard basis. What really confuses me is when we have to compute matrix with respect to non standard basis
Thanks for this wonderful explanation.
My exams is in an hour time, wish me good luck guys.
Great explanation of the interaction between matrices and vectors.
this video has been very helpful to me :)
IT WAS HELPFUL TO ME
Thank you so much, you made my life easier.
wonderful explaination.
thank you:)
I would have loved to find this video before my linear algebra final exam.
unfortunately in terms of polynomials this method doesn't work properly (if sb figured out why, please reply my comment), its' output is 90 degrees flipped matrix. Correct way is to write (x1, x2, x3) as matrix
([1,0,0],
[0,1,0],
[0,0,1])
then do the operation as for 4:46:
(1/2, 0, 1)
(1, 1, 1)
(1, -1, 1/4) and now these vectors write in columns, so:
[1/2, 1, 1]
[0, 1, -1]
[1, 1, 1/4]
this made it really simple thanks!
EZ situation, does the same apply when R3 to R2
Nice shortcut❤❤
Where's the transformation in the second example? We went from R^3 to R^3 , shouldn't transformations change the dimensions?
In the first example we get 3 equations from 2 variables so it's increased dimensions
But in the 2nd example we get 3 variables and turn it into 3 equations so the dimension doesn't change
Nice explanation
now i understand it ! thank you !
Such a clear explanation ❤ great work🙌🙏❤️
Thank you so much bro!
Thank you sir
you are welcome!
Thank you so much!
Can you do the question to find the matrix with the respect of standard basis of R^2 and R^3 please ? I could not understand what I need to do with standard basis ! Thanks
Is this map surjective?? If not pls explain why?
@cjjk9142 but dim V = dim W , I think it's necessary not sufficient condition for a map to be surjective. If a map is surjective then obviously both domain and co-domain must have same dimension but I don't think it's inverse is always true. For a map to be surjective the condition was ImT = W.
Is this same for finding Matrix of linear transformation with respect to standard basis?
Very helpful... danke!
Dear sorcerer, should algebra and trig be mastered to learn linear algebra? Thanks in advance
Trigonometry hardly comes up in linear algebra 1, you need to understand the cosine function for angles between vectors and you need to understand the sine function as well for rotation matrices but it's all rather basic trigonometry. In terms of algebra, I assume you mean the manipulation of equations and not algebra concerning group theory etcetera. Yes understanding basic algebra is important but you don't need to "master" it. That being said linear algebra is a new algebra with all kinds of different rules which are very interesting and useful tools for later in your math career. It was one of my favourite courses so far.
I would say if you can understand the derivation of a rotation matrix you probably know enough trig. There is a good video about it from Khan Academy and I’m sure from other places. That was the most trig I saw used in linear algebra other than being familiar with sine and cosine for the scalar product and cross product. Although that is more of a calc 3 thing.
@@gustopher6500 how much basic algebra do I need please? Only the rules and properties of functions and graphs and linear equations? Because in a lot of books like the one by Hoffman and Kunze and the other one by Anton they do make a small review. Thanks
@@mathpassion5902 I would say pre algebra is enough.
@@gustopher6500 and what is the best linear algebra book in your opinion for computer science and math that has good explanations and good exercises and examples? Thanks in advance
Thanks a lot
Shouldn't you be multiplying the linear transformation matrix by the transpose of x(x1, x2, x3)?
He did, he wrote vector x as a column matrix.
THANK YOU SO MUCHHHHHHHHHHHHHHHHH!!!!!!
Thank you boss!
very neat!
what does mapping R2 to R3 mean in geometric way?
R2 converted r3
Nice
i envy your handwriting
So much easier
Get the associated matrix *
You saved my life, I would kill myself, if I can't figure it out
Bruh my teacher told me to find the associated matrix of a transposition...
How you know if it inverse?