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.
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!
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
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
@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.
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
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 ?
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
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!
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
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
Thank you for your time and effort to teach this.
11 months later, it's still useful to someone in de world. Thanks 🙏🏿
Thanks very much!!! you made it really easier to understand than my lecturer's explanation 🙇♀️
👍👍
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 !!
this video has been very helpful to me :)
Great explanation of the interaction between matrices and vectors.
EZ situation, does the same apply when R3 to R2
Thank you so much, you made my life easier.
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 shortcut❤❤
wonderful explaination.
thank you:)
this made it really simple thanks!
Thanks for this wonderful explanation.
My exams is in an hour time, wish me good luck guys.
Such a clear explanation ❤ great work🙌🙏❤️
Nice explanation
I would have loved to find this video before my linear algebra final exam.
Thank you so much bro!
now i understand it ! thank you !
Thank you so much!
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.
Thank you sir
you are welcome!
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
Very helpful... danke!
Is this same for finding Matrix of linear transformation with respect to standard basis?
Thanks a lot
THANK YOU SO MUCHHHHHHHHHHHHHHHHH!!!!!!
Thank you boss!
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.
How you know if it inverse?
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
very neat!
what does mapping R2 to R3 mean in geometric way?
R2 converted r3
i envy your handwriting
Nice
So much easier
You saved my life, I would kill myself, if I can't figure it out
Get the associated matrix *
Bruh my teacher told me to find the associated matrix of a transposition...