How to Find the Matrix of a Linear Transformation

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How to Find the Matrix of a Linear Transformation

Рет қаралды 139,304

2 жыл бұрын

This is a very elementary discussion of linear transformations and matrices. I mention nothing about bases in this video and just give an easy way to identify the matrix. Hopefully this helps someone.
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Thank you:)

Пікірлер: 63

@alokraj8972 Жыл бұрын

Exactly what I want to understand. Like how we can represent a function or mapping or transformation in form of Matrix. Thanks a lot 🙏🏻

@jingyiwang5113 Жыл бұрын

You have provided a clear solution. It is so wise and kind of you to help me with my studies!

@user-ru3mx9zn3k 5 ай бұрын

are you student ?

@jacobharris5894 2 жыл бұрын

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.

@maxpercer7119 Жыл бұрын

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.

@davidpostiff7577 10 ай бұрын

@jacobharris5894 thanks great comment screenshotted this lol

@reamabdulsalam524 10 ай бұрын

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

@cubbyhoo 2 жыл бұрын

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!

@5Martian5 Жыл бұрын

Thank you! Very easy to understand! I definitely needed this!!!!!!

@TheMathSorcerer Жыл бұрын

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.

@barnabasmuluboka2543 Жыл бұрын

@@TheMathSorcerer I think you have the best video on this topic

@user-hp7pq1fh1g 15 күн бұрын

wonderful explaination.

@TheMathSorcerer 15 күн бұрын

thank you:)

@vikpusplug5694 Жыл бұрын

11 months later, it's still useful to someone in de world. Thanks 🙏🏿

@Amapolabearr 8 ай бұрын

thank you! i didnt realize how easy it was until you showed us !!

@Tomas-zv2js 2 ай бұрын

Thank you so much bro!

@huwaidaadillya9631 6 ай бұрын

Thanks very much!!! you made it really easier to understand than my lecturer's explanation 🙇‍♀️

@nisrinasyifa2842 6 ай бұрын

👍👍

@navinyaypatil9659 Жыл бұрын

Thanks a lot sir . Your videos have been so helpful to me.🙏🙏lots of love and support from India 🇮🇳 ❤️

@baneofthewilds5702 3 ай бұрын

this made it really simple thanks!

@whiteshadow5881 11 ай бұрын

EZ situation, does the same apply when R3 to R2

@italianodoc8161 Жыл бұрын

Thank you so much, you made my life easier.

@akashizhere322 3 ай бұрын

Very helpful... danke!

@Hasanlyno.1fan 9 ай бұрын

Where's the transformation in the second example? We went from R^3 to R^3 , shouldn't transformations change the dimensions?

@hellheaven4167 3 ай бұрын

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

@harpreet.002 7 ай бұрын

Such a clear explanation ❤ great work🙌🙏❤️

@dansedanse1173 5 ай бұрын

now i understand it ! thank you !

@kmviews928 3 ай бұрын

Thanks for this wonderful explanation. My exams is in an hour time, wish me good luck guys.

@chyldstudios 2 жыл бұрын

Great explanation of the interaction between matrices and vectors.

@ehmedlivasif3565 3 ай бұрын

Thanks a lot

@JaspreetSingh-zp2nm 11 ай бұрын

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

@MBoy2000_ 9 ай бұрын

this video has been very helpful to me :)

@somnath3986 9 ай бұрын

Is this map surjective?? If not pls explain why?

@somnath3986 7 ай бұрын

@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.

@abhisheks5625 6 ай бұрын

Nice explanation

@matthevandenberg 8 ай бұрын

Thank you so much!

@crispeto_2767 8 ай бұрын

I would have loved to find this video before my linear algebra final exam.

@tejasmonteiro2704 10 ай бұрын

Nice shortcut❤❤

@reamabdulsalam524 10 ай бұрын

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

@drewross3221 Жыл бұрын

Thank you boss!

@soyatoya2802 Жыл бұрын

Thank you sir

@TheMathSorcerer Жыл бұрын

you are welcome!

@mra9347 8 ай бұрын

THANK YOU SO MUCHHHHHHHHHHHHHHHHH!!!!!!

@xaej1he144 Жыл бұрын

Is this same for finding Matrix of linear transformation with respect to standard basis?

@barclayswsltv 8 ай бұрын

Nice

@morganmitchell4017 2 жыл бұрын

Shouldn't you be multiplying the linear transformation matrix by the transpose of x(x1, x2, x3)?

@audience2 7 ай бұрын

He did, he wrote vector x as a column matrix.

@ayushwithasingle_a Жыл бұрын

what does mapping R2 to R3 mean in geometric way?

@maxpercer7119 Жыл бұрын

very neat!

@raj-thebeastofficial9582 5 ай бұрын

@mathpassion5902 2 жыл бұрын

Dear sorcerer, should algebra and trig be mastered to learn linear algebra? Thanks in advance

@gustopher6500 2 жыл бұрын

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.

@jacobharris5894 2 жыл бұрын

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.

@mathpassion5902 2 жыл бұрын

@@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 2 жыл бұрын

@@mathpassion5902 I would say pre algebra is enough.

@mathpassion5902 2 жыл бұрын

@@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