Left inverse and right matrix inverses

This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.
More info here: www.udemy.com/...

[@stefanoppliger2931]

At minute 8:02 shouldn't it be m

[@mikexcohen1]

Hi Stefan. Good catch! You're right. Clearly, I copied that from a few slides earlier but forgot to change it.

[@jazbashaikh7454]

Thank you Mile COhen. It was very informative and nicely explained video. Can you give the code you just used to explain it? Or does anyone know if that kind of matlab code is available on internet, I'm new to matlab and the mathematics.

[@mohsinali-10]

Excellent explanation. Thank you!

[@maddisonvandenheuvel8840]

what does full rank mean?

[@mikexcohen1]

Rank is a number associated with a matrix that reveals the maximum number of columns (or rows) that can form a linearly independent set. For example, two vectors [1 2] and [2 4] are dependent, because you can create one by multiplying the other by a single number. A second example: [1 2] and [1 3]. You cannot create one vector from the other. Putting the first two vectors into a matrix will have a rank=1, whereas the second example would form a rank=2 matrix. Note that this video is taken from a course on linear algebra, so some concepts are explained in earlier videos.

[@saimakhalil5137]

loveeeeeeeeeeeeeeeeeeee

[@bliezz]

Thankyou for making this video, it helps me a lot :') studying it in college doesn't make me understand as much as i can understand it from u in less than 30 mins

[@김종엽-u5c]

Thank you, umm I have ques about mn. why they don't include m=n?

[@mikexcohen1]

when m=n, then you don't need the one-sided inverse; you can use the regular inverse.

[@hearthacker5565]

@@mikexcohen1 hahahaha sir this man even forget regular inverse. He get so much serious about notations 🤣🤣🤣. By the way may Allah bless you sir. I was not able to understand this concept.

[@muhammadabdurrehman878]

@@mikexcohen1 when m=n singular square matrix then how to find inverse

[@shreejanshrestha1931]

@@muhammadabdurrehman878 There is something known as pseudo inverse. For this, you need to have a concept of SVD. I GUESS...

[@vanshtomar6527]

@@muhammadabdurrehman878 if matrix is singular then I guess it's inverse doesn't exist

[@ryanjackson0x]

Does A^T have to be used in order to get the left or right inverse?

[@jinkijung6401]

Thank you. Somewhere you mentioned this has huge potential applications. Could you please give me a possible use case ? I came to this video while I was searching solution for "determinant of tall matrix".

[@mikexcohen1]

The left inverse is used to find solutions to systems of equations, so it's used all the time in statistics, machine-learning, optimization, control engineering, and so on.

[@minyezhang2981]

Thanks for the video! Inspiring idea to represent left/right inverse by a and aT.

[@mingyuemiao2757]

Thank you Mike X Cohen, it is very clearly explained video.

[@mikexcohen1]

You are very welcome, Miao.

[@gisellaadara5944]

Thank you for making this video! :")

[@JiteshKumar-yd1cx]

Not clear explanation

[@iammouliroy]

wow.. thank you..

[@ImmunityG]

Is it possible to find the right inverse for this? A = ( 0 1 0 1 ) (0 0 1 0 ) Note: This is in binary so if you get it to 2, that just puts it back to 0. I'm doing a past exam and im supposed to find the right inverse for this but I'm getting: I was able to Transpose A but when I multiply them by each other I get: (0 0) (0 1) which is not invertible (and inverting it is supposed to be the next step. I'm mainly asking to check if I did any mistakes

[@ghazalkhaleghei9451]

that was so helpful, thanks a lot!!!

[@mikexcohen1]

You're welcome!